Sin 30 x cos 45° + sin go x sin

Berikut ini adalah pertanyaan dari sitirayhanwirda pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Atas

Sin 30 x cos 45° + sin go x sin 45° / Jawabs

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

nilai dari Sin 30° x cos 45° + sin 90° x sin 45° adalah $\bf{\frac{3}{4}\sqrt{2}}$

$\:$

Trigonometri

Pendahuluan

A.) Definisi

.) Perbandingan Trigonometri

Pada segitiga siku-siku ABC, berlaku :

*Gambar ke-1

$\small\mathbf{\left(a.\right)\ \ \sin\alpha=\frac{y}{r}=\frac{de}{mi}}$

$\small\mathbf{\left(b.\right)\ \ \cos\alpha=\frac{x}{r}=\frac{sa}{mi}}$

$\small\mathbf{\left(c.\right)\ \ \tan\alpha=\frac{y}{x}=\frac{de}{sa}}$

$\small\mathbf{\left(d.\right)\ \ \csc\alpha=\frac{1}{\sin\alpha}=\frac{r}{y}}$

$\small\mathbf{\left(e.\right)\ \ \sec\alpha=\frac{1}{\cos\alpha}=\frac{r}{x}}$

$\small\mathbf{\left(f.\right)\ \ \cot\alpha=\frac{1}{\tan\alpha}=\frac{y}{x}}$

B.) Sudut dan Kuadran

1.) Pembagian Daerah

$\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{I}}&\underline{\mathbf{II}}&\underline{\mathbf{III}}&\underline{\mathbf{IV}}\\&&&\\\mathbf{absis(x)}&\mathbf{+}&\mathbf{-}&\mathbf{-}&\mathbf{+}\\&&&\\\mathbf{Ordinat(y)}&\mathbf{+}&\mathbf{+}&\mathbf{-}&\mathbf{-}\end{array}}$

2.) Tanda-tanda Fungsi

$\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{I}}&\underline{\mathbf{II}}&\underline{\mathbf{III}}&\underline{\mathbf{IV}}\\&&&\\\mathbf{sin}&\mathbf{+}&\mathbf{+}&\mathbf{-}&\mathbf{-}\\&&&\\\mathbf{cos}&\mathbf{+}&\mathbf{-}&\mathbf{-}&\mathbf{+}\\&&&\\\mathbf{tan}&\mathbf{+}&\mathbf{-}&\mathbf{+}&\mathbf{-}\end{array}}$

3.) Sudut-sudut Istimewa

$\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{0^{\circ}}}&\underline{\mathbf{30^{\circ}}}&\underline{\mathbf{45^{\circ}}}&\underline{\mathbf{60^{\circ}}}\\&&&\\\mathbf{sin}&\mathbf{0}&\mathbf{\frac{1}{2}}&\mathbf{\frac{1}{2}\sqrt{2}}&\mathbf{\frac{1}{2}\sqrt{3}}\\&&&\\\mathbf{cos}&\mathbf{1}&\mathbf{\frac{1}{2}\sqrt{3}}&\mathbf{\frac{1}{2}\sqrt{2}}&\mathbf{\frac{1}{2}}\\&&&\\\mathbf{tan}&\mathbf{0}&\mathbf{\frac{1}{3}\sqrt{3}}&\mathbf{1}&\mathbf{\sqrt{3}}\end{array}}$ $\boxed{\begin{array}{c}\underline{\mathbf{90^{\circ}}}\\\\\mathbf{1}\\\\\mathbf{0}\\\\\infty\end{array}}$

4.) Sudut Berelasi

a. Kalau kita gunakan (90°± ...) atau (270°± ...)

1.) Fungsi berubah

$\boxed{\begin{array}{c|c}\underline{\mathbf{Mula-mula}}&\underline{\mathbf{Perubahan}}\\\\\mathbf{sin}&\mathbf{+/-cos}\\\\\mathbf{cos}&\mathbf{+/-sin}\\\\\mathbf{tan}&\mathbf{+/-cot}\end{array}}$

2.) Tanda +/- mengikuti kuadran

b. kalau kita gunakan (180°± ...) atau (360°− ...)

1.) Fungsi tetap

$\boxed{\begin{array}{c|c}\underline{\mathbf{Mula-mula}}&\underline{\mathbf{Perubahan}}\\\\\mathbf{sin}&\mathbf{+/-sin}\\\\\mathbf{cos}&\mathbf{+/-cos}\\\\\mathbf{tan}&\mathbf{+/-tan}\end{array}}$

C.) Dalil Segitiga

1.) Aturan Sinus

*gambar ke-2

$\small\mathbf{\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}}$

2.) Aturan Cosinus

a. a² = b² + c² - 2bc cos A atau

$\small\mathbf{cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}}$

b. b² = a² + c² - 2ac cos B atau

$\small\mathbf{cos B=\frac{a^{2}+c^{2}-b^{2}}{2ac}}$

c. c² = a² + b² - 2ab cos C atau

$\small\mathbf{cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}}$

$\:$

Pembahasan

Diketahui :

$\bf{\sin\left(30^{\circ}\right)\times\cos\left(45^{\circ}\right)+\sin\left(90^{\circ}\right)\times\sin\left(45^{\circ}\right)}$

Ditanya :

berapa nilai tersebut?

Jawaban :

$\bf{\sin\left(30^{\circ}\right)\times\cos\left(45^{\circ}\right)+\sin\left(90^{\circ}\right)\times\sin\left(45^{\circ}\right)}$

$\bf{=\frac{1}{2}\times\frac{1}{2}\sqrt{2}+1\times\frac{1}{2}\sqrt{2}}$

$\bf{=\frac{1}{4}\sqrt{2}+\frac{1}{2}\sqrt{2}}$

$\bf{=\frac{1}{4}\sqrt{2}+\frac{2}{4}\sqrt{2}}$

$\boxed{\bf{=\frac{3}{4}\sqrt{2}}}$

$\:$

Pelajari Lebih Lanjut :

Contoh soal mencari sisi samping : yomemimo.com/tugas/48680192

Nilai dari cos²45° + sin²240° = : yomemimo.com/tugas/52094991

Jika cos (72,24°) = 1/5. maka sin (17,76°) ialah : yomemimo.com/tugas/52659460

Berapakah sin(30°) × cos(60°) : yomemimo.com/tugas/52206983

Jika A+B = 30°, maka Cos A ialah : yomemimo.com/tugas/52680527

$\:$

Detail Jawaban :

Grade : SMA

Kode Kategorisasi : 10.2.6

Kelas : 10

Kode Mapel : 2

Pelajaran : Matematika

Bab : 6

Sub Bab : Bab 6 – Trigonometri Dasar

$\:$

Kata Kunci : Trigonometri dasar, sin, cos, tan.

$nilai dari Sin 30° x cos 45° + sin 90° x sin 45° adalah [tex]\bf{\frac{3}{4}\sqrt{2}}[/tex][tex] \: [/tex]TrigonometriPendahuluanA.) Definisi .) Perbandingan TrigonometriPada segitiga siku-siku ABC, berlaku : *Gambar ke-1[tex]\small\mathbf{\left(a.\right)\ \ \sin\alpha=\frac{y}{r}=\frac{de}{mi}} [/tex][tex]\small\mathbf{\left(b.\right)\ \ \cos\alpha=\frac{x}{r}=\frac{sa}{mi}} [/tex][tex]\small\mathbf{\left(c.\right)\ \ \tan\alpha=\frac{y}{x}=\frac{de}{sa}} [/tex][tex]\small\mathbf{\left(d.\right)\ \ \csc\alpha=\frac{1}{\sin\alpha}=\frac{r}{y}}[/tex][tex]\small\mathbf{\left(e.\right)\ \ \sec\alpha=\frac{1}{\cos\alpha}=\frac{r}{x}}[/tex][tex]\small\mathbf{\left(f.\right)\ \ \cot\alpha=\frac{1}{\tan\alpha}=\frac{y}{x}}[/tex]B.) Sudut dan Kuadran1.) Pembagian Daerah [tex]\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{I}}&\underline{\mathbf{II}}&\underline{\mathbf{III}}&\underline{\mathbf{IV}}\\&&&\\\mathbf{absis(x)}&\mathbf{+}&\mathbf{-}&\mathbf{-}&\mathbf{+}\\&&&\\\mathbf{Ordinat(y)}&\mathbf{+}&\mathbf{+}&\mathbf{-}&\mathbf{-}\end{array}}[/tex]2.) Tanda-tanda Fungsi[tex]\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{I}}&\underline{\mathbf{II}}&\underline{\mathbf{III}}&\underline{\mathbf{IV}}\\&&&\\\mathbf{sin}&\mathbf{+}&\mathbf{+}&\mathbf{-}&\mathbf{-}\\&&&\\\mathbf{cos}&\mathbf{+}&\mathbf{-}&\mathbf{-}&\mathbf{+}\\&&&\\\mathbf{tan}&\mathbf{+}&\mathbf{-}&\mathbf{+}&\mathbf{-}\end{array}}[/tex]3.) Sudut-sudut Istimewa[tex]\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{0^{\circ}}}&\underline{\mathbf{30^{\circ}}}&\underline{\mathbf{45^{\circ}}}&\underline{\mathbf{60^{\circ}}}\\&&&\\\mathbf{sin}&\mathbf{0}&\mathbf{\frac{1}{2}}&\mathbf{\frac{1}{2}\sqrt{2}}&\mathbf{\frac{1}{2}\sqrt{3}}\\&&&\\\mathbf{cos}&\mathbf{1}&\mathbf{\frac{1}{2}\sqrt{3}}&\mathbf{\frac{1}{2}\sqrt{2}}&\mathbf{\frac{1}{2}}\\&&&\\\mathbf{tan}&\mathbf{0}&\mathbf{\frac{1}{3}\sqrt{3}}&\mathbf{1}&\mathbf{\sqrt{3}}\end{array}} [/tex] [tex] \boxed{\begin{array}{c}\underline{\mathbf{90^{\circ}}}\\\\\mathbf{1}\\\\\mathbf{0}\\\\\infty\end{array}} [/tex]4.) Sudut Berelasia. Kalau kita gunakan (90°± ...) atau (270°± ...) 1.) Fungsi berubah [tex]\boxed{\begin{array}{c|c}\underline{\mathbf{Mula-mula}}&\underline{\mathbf{Perubahan}}\\\\\mathbf{sin}&\mathbf{+/-cos}\\\\\mathbf{cos}&\mathbf{+/-sin}\\\\\mathbf{tan}&\mathbf{+/-cot}\end{array}}[/tex] 2.) Tanda +/- mengikuti kuadranb. kalau kita gunakan (180°± ...) atau (360°− ...) 1.) Fungsi tetap[tex]\boxed{\begin{array}{c|c}\underline{\mathbf{Mula-mula}}&\underline{\mathbf{Perubahan}}\\\\\mathbf{sin}&\mathbf{+/-sin}\\\\\mathbf{cos}&\mathbf{+/-cos}\\\\\mathbf{tan}&\mathbf{+/-tan}\end{array}}[/tex]C.) Dalil Segitiga1.) Aturan Sinus*gambar ke-2[tex]\small\mathbf{\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}}[/tex]2.) Aturan Cosinusa. a² = b² + c² - 2bc cos A atau [tex]\small\mathbf{cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}}[/tex]b. b² = a² + c² - 2ac cos B atau [tex]\small\mathbf{cos B=\frac{a^{2}+c^{2}-b^{2}}{2ac}}[/tex]c. c² = a² + b² - 2ab cos C atau [tex]\small\mathbf{cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}}[/tex][tex] \: [/tex][tex] \: [/tex]PembahasanDiketahui :[tex]\bf{\sin\left(30^{\circ}\right)\times\cos\left(45^{\circ}\right)+\sin\left(90^{\circ}\right)\times\sin\left(45^{\circ}\right)}[/tex]Ditanya :berapa nilai tersebut?Jawaban :[tex]\bf{\sin\left(30^{\circ}\right)\times\cos\left(45^{\circ}\right)+\sin\left(90^{\circ}\right)\times\sin\left(45^{\circ}\right)}[/tex][tex]\bf{=\frac{1}{2}\times\frac{1}{2}\sqrt{2}+1\times\frac{1}{2}\sqrt{2}}[/tex][tex]\bf{=\frac{1}{4}\sqrt{2}+\frac{1}{2}\sqrt{2}}[/tex][tex]\bf{=\frac{1}{4}\sqrt{2}+\frac{2}{4}\sqrt{2}}[/tex][tex]\boxed{\bf{=\frac{3}{4}\sqrt{2}}}[/tex][tex] \: [/tex][tex] \: [/tex]Pelajari Lebih Lanjut :Contoh soal mencari sisi samping : https://brainly.co.id/tugas/48680192Nilai dari cos²45° + sin²240° = : https://brainly.co.id/tugas/52094991Jika cos (72,24°) = 1/5. maka sin (17,76°) ialah : https://brainly.co.id/tugas/52659460Berapakah sin(30°) × cos(60°) : https://brainly.co.id/tugas/52206983Jika A+B = 30°, maka Cos A ialah : https://brainly.co.id/tugas/52680527 [tex] \: [/tex][tex] \: [/tex]Detail Jawaban :Grade : SMAKode Kategorisasi : 10.2.6Kelas : 10Kode Mapel : 2Pelajaran : MatematikaBab : 6Sub Bab : Bab 6 – Trigonometri Dasar[tex] \: [/tex]Kata Kunci : Trigonometri dasar, sin, cos, tan.$ $nilai dari Sin 30° x cos 45° + sin 90° x sin 45° adalah [tex]\bf{\frac{3}{4}\sqrt{2}}[/tex][tex] \: [/tex]TrigonometriPendahuluanA.) Definisi .) Perbandingan TrigonometriPada segitiga siku-siku ABC, berlaku : *Gambar ke-1[tex]\small\mathbf{\left(a.\right)\ \ \sin\alpha=\frac{y}{r}=\frac{de}{mi}} [/tex][tex]\small\mathbf{\left(b.\right)\ \ \cos\alpha=\frac{x}{r}=\frac{sa}{mi}} [/tex][tex]\small\mathbf{\left(c.\right)\ \ \tan\alpha=\frac{y}{x}=\frac{de}{sa}} [/tex][tex]\small\mathbf{\left(d.\right)\ \ \csc\alpha=\frac{1}{\sin\alpha}=\frac{r}{y}}[/tex][tex]\small\mathbf{\left(e.\right)\ \ \sec\alpha=\frac{1}{\cos\alpha}=\frac{r}{x}}[/tex][tex]\small\mathbf{\left(f.\right)\ \ \cot\alpha=\frac{1}{\tan\alpha}=\frac{y}{x}}[/tex]B.) Sudut dan Kuadran1.) Pembagian Daerah [tex]\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{I}}&\underline{\mathbf{II}}&\underline{\mathbf{III}}&\underline{\mathbf{IV}}\\&&&\\\mathbf{absis(x)}&\mathbf{+}&\mathbf{-}&\mathbf{-}&\mathbf{+}\\&&&\\\mathbf{Ordinat(y)}&\mathbf{+}&\mathbf{+}&\mathbf{-}&\mathbf{-}\end{array}}[/tex]2.) Tanda-tanda Fungsi[tex]\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{I}}&\underline{\mathbf{II}}&\underline{\mathbf{III}}&\underline{\mathbf{IV}}\\&&&\\\mathbf{sin}&\mathbf{+}&\mathbf{+}&\mathbf{-}&\mathbf{-}\\&&&\\\mathbf{cos}&\mathbf{+}&\mathbf{-}&\mathbf{-}&\mathbf{+}\\&&&\\\mathbf{tan}&\mathbf{+}&\mathbf{-}&\mathbf{+}&\mathbf{-}\end{array}}[/tex]3.) Sudut-sudut Istimewa[tex]\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{0^{\circ}}}&\underline{\mathbf{30^{\circ}}}&\underline{\mathbf{45^{\circ}}}&\underline{\mathbf{60^{\circ}}}\\&&&\\\mathbf{sin}&\mathbf{0}&\mathbf{\frac{1}{2}}&\mathbf{\frac{1}{2}\sqrt{2}}&\mathbf{\frac{1}{2}\sqrt{3}}\\&&&\\\mathbf{cos}&\mathbf{1}&\mathbf{\frac{1}{2}\sqrt{3}}&\mathbf{\frac{1}{2}\sqrt{2}}&\mathbf{\frac{1}{2}}\\&&&\\\mathbf{tan}&\mathbf{0}&\mathbf{\frac{1}{3}\sqrt{3}}&\mathbf{1}&\mathbf{\sqrt{3}}\end{array}} [/tex] [tex] \boxed{\begin{array}{c}\underline{\mathbf{90^{\circ}}}\\\\\mathbf{1}\\\\\mathbf{0}\\\\\infty\end{array}} [/tex]4.) Sudut Berelasia. Kalau kita gunakan (90°± ...) atau (270°± ...) 1.) Fungsi berubah [tex]\boxed{\begin{array}{c|c}\underline{\mathbf{Mula-mula}}&\underline{\mathbf{Perubahan}}\\\\\mathbf{sin}&\mathbf{+/-cos}\\\\\mathbf{cos}&\mathbf{+/-sin}\\\\\mathbf{tan}&\mathbf{+/-cot}\end{array}}[/tex] 2.) Tanda +/- mengikuti kuadranb. kalau kita gunakan (180°± ...) atau (360°− ...) 1.) Fungsi tetap[tex]\boxed{\begin{array}{c|c}\underline{\mathbf{Mula-mula}}&\underline{\mathbf{Perubahan}}\\\\\mathbf{sin}&\mathbf{+/-sin}\\\\\mathbf{cos}&\mathbf{+/-cos}\\\\\mathbf{tan}&\mathbf{+/-tan}\end{array}}[/tex]C.) Dalil Segitiga1.) Aturan Sinus*gambar ke-2[tex]\small\mathbf{\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}}[/tex]2.) Aturan Cosinusa. a² = b² + c² - 2bc cos A atau [tex]\small\mathbf{cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}}[/tex]b. b² = a² + c² - 2ac cos B atau [tex]\small\mathbf{cos B=\frac{a^{2}+c^{2}-b^{2}}{2ac}}[/tex]c. c² = a² + b² - 2ab cos C atau [tex]\small\mathbf{cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}}[/tex][tex] \: [/tex][tex] \: [/tex]PembahasanDiketahui :[tex]\bf{\sin\left(30^{\circ}\right)\times\cos\left(45^{\circ}\right)+\sin\left(90^{\circ}\right)\times\sin\left(45^{\circ}\right)}[/tex]Ditanya :berapa nilai tersebut?Jawaban :[tex]\bf{\sin\left(30^{\circ}\right)\times\cos\left(45^{\circ}\right)+\sin\left(90^{\circ}\right)\times\sin\left(45^{\circ}\right)}[/tex][tex]\bf{=\frac{1}{2}\times\frac{1}{2}\sqrt{2}+1\times\frac{1}{2}\sqrt{2}}[/tex][tex]\bf{=\frac{1}{4}\sqrt{2}+\frac{1}{2}\sqrt{2}}[/tex][tex]\bf{=\frac{1}{4}\sqrt{2}+\frac{2}{4}\sqrt{2}}[/tex][tex]\boxed{\bf{=\frac{3}{4}\sqrt{2}}}[/tex][tex] \: [/tex][tex] \: [/tex]Pelajari Lebih Lanjut :Contoh soal mencari sisi samping : https://brainly.co.id/tugas/48680192Nilai dari cos²45° + sin²240° = : https://brainly.co.id/tugas/52094991Jika cos (72,24°) = 1/5. maka sin (17,76°) ialah : https://brainly.co.id/tugas/52659460Berapakah sin(30°) × cos(60°) : https://brainly.co.id/tugas/52206983Jika A+B = 30°, maka Cos A ialah : https://brainly.co.id/tugas/52680527 [tex] \: [/tex][tex] \: [/tex]Detail Jawaban :Grade : SMAKode Kategorisasi : 10.2.6Kelas : 10Kode Mapel : 2Pelajaran : MatematikaBab : 6Sub Bab : Bab 6 – Trigonometri Dasar[tex] \: [/tex]Kata Kunci : Trigonometri dasar, sin, cos, tan.$ $nilai dari Sin 30° x cos 45° + sin 90° x sin 45° adalah [tex]\bf{\frac{3}{4}\sqrt{2}}[/tex][tex] \: [/tex]TrigonometriPendahuluanA.) Definisi .) Perbandingan TrigonometriPada segitiga siku-siku ABC, berlaku : *Gambar ke-1[tex]\small\mathbf{\left(a.\right)\ \ \sin\alpha=\frac{y}{r}=\frac{de}{mi}} [/tex][tex]\small\mathbf{\left(b.\right)\ \ \cos\alpha=\frac{x}{r}=\frac{sa}{mi}} [/tex][tex]\small\mathbf{\left(c.\right)\ \ \tan\alpha=\frac{y}{x}=\frac{de}{sa}} [/tex][tex]\small\mathbf{\left(d.\right)\ \ \csc\alpha=\frac{1}{\sin\alpha}=\frac{r}{y}}[/tex][tex]\small\mathbf{\left(e.\right)\ \ \sec\alpha=\frac{1}{\cos\alpha}=\frac{r}{x}}[/tex][tex]\small\mathbf{\left(f.\right)\ \ \cot\alpha=\frac{1}{\tan\alpha}=\frac{y}{x}}[/tex]B.) Sudut dan Kuadran1.) Pembagian Daerah [tex]\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{I}}&\underline{\mathbf{II}}&\underline{\mathbf{III}}&\underline{\mathbf{IV}}\\&&&\\\mathbf{absis(x)}&\mathbf{+}&\mathbf{-}&\mathbf{-}&\mathbf{+}\\&&&\\\mathbf{Ordinat(y)}&\mathbf{+}&\mathbf{+}&\mathbf{-}&\mathbf{-}\end{array}}[/tex]2.) Tanda-tanda Fungsi[tex]\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{I}}&\underline{\mathbf{II}}&\underline{\mathbf{III}}&\underline{\mathbf{IV}}\\&&&\\\mathbf{sin}&\mathbf{+}&\mathbf{+}&\mathbf{-}&\mathbf{-}\\&&&\\\mathbf{cos}&\mathbf{+}&\mathbf{-}&\mathbf{-}&\mathbf{+}\\&&&\\\mathbf{tan}&\mathbf{+}&\mathbf{-}&\mathbf{+}&\mathbf{-}\end{array}}[/tex]3.) Sudut-sudut Istimewa[tex]\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{0^{\circ}}}&\underline{\mathbf{30^{\circ}}}&\underline{\mathbf{45^{\circ}}}&\underline{\mathbf{60^{\circ}}}\\&&&\\\mathbf{sin}&\mathbf{0}&\mathbf{\frac{1}{2}}&\mathbf{\frac{1}{2}\sqrt{2}}&\mathbf{\frac{1}{2}\sqrt{3}}\\&&&\\\mathbf{cos}&\mathbf{1}&\mathbf{\frac{1}{2}\sqrt{3}}&\mathbf{\frac{1}{2}\sqrt{2}}&\mathbf{\frac{1}{2}}\\&&&\\\mathbf{tan}&\mathbf{0}&\mathbf{\frac{1}{3}\sqrt{3}}&\mathbf{1}&\mathbf{\sqrt{3}}\end{array}} [/tex] [tex] \boxed{\begin{array}{c}\underline{\mathbf{90^{\circ}}}\\\\\mathbf{1}\\\\\mathbf{0}\\\\\infty\end{array}} [/tex]4.) Sudut Berelasia. Kalau kita gunakan (90°± ...) atau (270°± ...) 1.) Fungsi berubah [tex]\boxed{\begin{array}{c|c}\underline{\mathbf{Mula-mula}}&\underline{\mathbf{Perubahan}}\\\\\mathbf{sin}&\mathbf{+/-cos}\\\\\mathbf{cos}&\mathbf{+/-sin}\\\\\mathbf{tan}&\mathbf{+/-cot}\end{array}}[/tex] 2.) Tanda +/- mengikuti kuadranb. kalau kita gunakan (180°± ...) atau (360°− ...) 1.) Fungsi tetap[tex]\boxed{\begin{array}{c|c}\underline{\mathbf{Mula-mula}}&\underline{\mathbf{Perubahan}}\\\\\mathbf{sin}&\mathbf{+/-sin}\\\\\mathbf{cos}&\mathbf{+/-cos}\\\\\mathbf{tan}&\mathbf{+/-tan}\end{array}}[/tex]C.) Dalil Segitiga1.) Aturan Sinus*gambar ke-2[tex]\small\mathbf{\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}}[/tex]2.) Aturan Cosinusa. a² = b² + c² - 2bc cos A atau [tex]\small\mathbf{cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}}[/tex]b. b² = a² + c² - 2ac cos B atau [tex]\small\mathbf{cos B=\frac{a^{2}+c^{2}-b^{2}}{2ac}}[/tex]c. c² = a² + b² - 2ab cos C atau [tex]\small\mathbf{cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}}[/tex][tex] \: [/tex][tex] \: [/tex]PembahasanDiketahui :[tex]\bf{\sin\left(30^{\circ}\right)\times\cos\left(45^{\circ}\right)+\sin\left(90^{\circ}\right)\times\sin\left(45^{\circ}\right)}[/tex]Ditanya :berapa nilai tersebut?Jawaban :[tex]\bf{\sin\left(30^{\circ}\right)\times\cos\left(45^{\circ}\right)+\sin\left(90^{\circ}\right)\times\sin\left(45^{\circ}\right)}[/tex][tex]\bf{=\frac{1}{2}\times\frac{1}{2}\sqrt{2}+1\times\frac{1}{2}\sqrt{2}}[/tex][tex]\bf{=\frac{1}{4}\sqrt{2}+\frac{1}{2}\sqrt{2}}[/tex][tex]\bf{=\frac{1}{4}\sqrt{2}+\frac{2}{4}\sqrt{2}}[/tex][tex]\boxed{\bf{=\frac{3}{4}\sqrt{2}}}[/tex][tex] \: [/tex][tex] \: [/tex]Pelajari Lebih Lanjut :Contoh soal mencari sisi samping : https://brainly.co.id/tugas/48680192Nilai dari cos²45° + sin²240° = : https://brainly.co.id/tugas/52094991Jika cos (72,24°) = 1/5. maka sin (17,76°) ialah : https://brainly.co.id/tugas/52659460Berapakah sin(30°) × cos(60°) : https://brainly.co.id/tugas/52206983Jika A+B = 30°, maka Cos A ialah : https://brainly.co.id/tugas/52680527 [tex] \: [/tex][tex] \: [/tex]Detail Jawaban :Grade : SMAKode Kategorisasi : 10.2.6Kelas : 10Kode Mapel : 2Pelajaran : MatematikaBab : 6Sub Bab : Bab 6 – Trigonometri Dasar[tex] \: [/tex]Kata Kunci : Trigonometri dasar, sin, cos, tan.$ $nilai dari Sin 30° x cos 45° + sin 90° x sin 45° adalah [tex]\bf{\frac{3}{4}\sqrt{2}}[/tex][tex] \: [/tex]TrigonometriPendahuluanA.) Definisi .) Perbandingan TrigonometriPada segitiga siku-siku ABC, berlaku : *Gambar ke-1[tex]\small\mathbf{\left(a.\right)\ \ \sin\alpha=\frac{y}{r}=\frac{de}{mi}} [/tex][tex]\small\mathbf{\left(b.\right)\ \ \cos\alpha=\frac{x}{r}=\frac{sa}{mi}} [/tex][tex]\small\mathbf{\left(c.\right)\ \ \tan\alpha=\frac{y}{x}=\frac{de}{sa}} [/tex][tex]\small\mathbf{\left(d.\right)\ \ \csc\alpha=\frac{1}{\sin\alpha}=\frac{r}{y}}[/tex][tex]\small\mathbf{\left(e.\right)\ \ \sec\alpha=\frac{1}{\cos\alpha}=\frac{r}{x}}[/tex][tex]\small\mathbf{\left(f.\right)\ \ \cot\alpha=\frac{1}{\tan\alpha}=\frac{y}{x}}[/tex]B.) Sudut dan Kuadran1.) Pembagian Daerah [tex]\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{I}}&\underline{\mathbf{II}}&\underline{\mathbf{III}}&\underline{\mathbf{IV}}\\&&&\\\mathbf{absis(x)}&\mathbf{+}&\mathbf{-}&\mathbf{-}&\mathbf{+}\\&&&\\\mathbf{Ordinat(y)}&\mathbf{+}&\mathbf{+}&\mathbf{-}&\mathbf{-}\end{array}}[/tex]2.) Tanda-tanda Fungsi[tex]\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{I}}&\underline{\mathbf{II}}&\underline{\mathbf{III}}&\underline{\mathbf{IV}}\\&&&\\\mathbf{sin}&\mathbf{+}&\mathbf{+}&\mathbf{-}&\mathbf{-}\\&&&\\\mathbf{cos}&\mathbf{+}&\mathbf{-}&\mathbf{-}&\mathbf{+}\\&&&\\\mathbf{tan}&\mathbf{+}&\mathbf{-}&\mathbf{+}&\mathbf{-}\end{array}}[/tex]3.) Sudut-sudut Istimewa[tex]\boxed{\begin{array}{c|c|c|c|c}\underline{\mathbf{Kuadran}}&\underline{\mathbf{0^{\circ}}}&\underline{\mathbf{30^{\circ}}}&\underline{\mathbf{45^{\circ}}}&\underline{\mathbf{60^{\circ}}}\\&&&\\\mathbf{sin}&\mathbf{0}&\mathbf{\frac{1}{2}}&\mathbf{\frac{1}{2}\sqrt{2}}&\mathbf{\frac{1}{2}\sqrt{3}}\\&&&\\\mathbf{cos}&\mathbf{1}&\mathbf{\frac{1}{2}\sqrt{3}}&\mathbf{\frac{1}{2}\sqrt{2}}&\mathbf{\frac{1}{2}}\\&&&\\\mathbf{tan}&\mathbf{0}&\mathbf{\frac{1}{3}\sqrt{3}}&\mathbf{1}&\mathbf{\sqrt{3}}\end{array}} [/tex] [tex] \boxed{\begin{array}{c}\underline{\mathbf{90^{\circ}}}\\\\\mathbf{1}\\\\\mathbf{0}\\\\\infty\end{array}} [/tex]4.) Sudut Berelasia. Kalau kita gunakan (90°± ...) atau (270°± ...) 1.) Fungsi berubah [tex]\boxed{\begin{array}{c|c}\underline{\mathbf{Mula-mula}}&\underline{\mathbf{Perubahan}}\\\\\mathbf{sin}&\mathbf{+/-cos}\\\\\mathbf{cos}&\mathbf{+/-sin}\\\\\mathbf{tan}&\mathbf{+/-cot}\end{array}}[/tex] 2.) Tanda +/- mengikuti kuadranb. kalau kita gunakan (180°± ...) atau (360°− ...) 1.) Fungsi tetap[tex]\boxed{\begin{array}{c|c}\underline{\mathbf{Mula-mula}}&\underline{\mathbf{Perubahan}}\\\\\mathbf{sin}&\mathbf{+/-sin}\\\\\mathbf{cos}&\mathbf{+/-cos}\\\\\mathbf{tan}&\mathbf{+/-tan}\end{array}}[/tex]C.) Dalil Segitiga1.) Aturan Sinus*gambar ke-2[tex]\small\mathbf{\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}}[/tex]2.) Aturan Cosinusa. a² = b² + c² - 2bc cos A atau [tex]\small\mathbf{cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}}[/tex]b. b² = a² + c² - 2ac cos B atau [tex]\small\mathbf{cos B=\frac{a^{2}+c^{2}-b^{2}}{2ac}}[/tex]c. c² = a² + b² - 2ab cos C atau [tex]\small\mathbf{cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}}[/tex][tex] \: [/tex][tex] \: [/tex]PembahasanDiketahui :[tex]\bf{\sin\left(30^{\circ}\right)\times\cos\left(45^{\circ}\right)+\sin\left(90^{\circ}\right)\times\sin\left(45^{\circ}\right)}[/tex]Ditanya :berapa nilai tersebut?Jawaban :[tex]\bf{\sin\left(30^{\circ}\right)\times\cos\left(45^{\circ}\right)+\sin\left(90^{\circ}\right)\times\sin\left(45^{\circ}\right)}[/tex][tex]\bf{=\frac{1}{2}\times\frac{1}{2}\sqrt{2}+1\times\frac{1}{2}\sqrt{2}}[/tex][tex]\bf{=\frac{1}{4}\sqrt{2}+\frac{1}{2}\sqrt{2}}[/tex][tex]\bf{=\frac{1}{4}\sqrt{2}+\frac{2}{4}\sqrt{2}}[/tex][tex]\boxed{\bf{=\frac{3}{4}\sqrt{2}}}[/tex][tex] \: [/tex][tex] \: [/tex]Pelajari Lebih Lanjut :Contoh soal mencari sisi samping : https://brainly.co.id/tugas/48680192Nilai dari cos²45° + sin²240° = : https://brainly.co.id/tugas/52094991Jika cos (72,24°) = 1/5. maka sin (17,76°) ialah : https://brainly.co.id/tugas/52659460Berapakah sin(30°) × cos(60°) : https://brainly.co.id/tugas/52206983Jika A+B = 30°, maka Cos A ialah : https://brainly.co.id/tugas/52680527 [tex] \: [/tex][tex] \: [/tex]Detail Jawaban :Grade : SMAKode Kategorisasi : 10.2.6Kelas : 10Kode Mapel : 2Pelajaran : MatematikaBab : 6Sub Bab : Bab 6 – Trigonometri Dasar[tex] \: [/tex]Kata Kunci : Trigonometri dasar, sin, cos, tan.$