Jawaban:

Kelas : X (1 SMA)

Materi : Trigonometri

Kata Kunci : Perbandingan, sudut

Pembahasan :

Dalam trigonometri, besar sudut α dibagi menjadi 4 kelompok, yaitu :

Kuadran I : 0° < α < 90° (0 < α < π/2)

sin (90° - α) = cos α

cos (90° - α) = sin α

tan (90° - α) = cotan α

cotan (90° - α) = tan α

secan (90° - α) = sec α

sec (90° - α) = cosec α

Kuadran II : 90° < α < 180° (π/2 < α < π)

sin (180° - α) = sin α

cos (180° - α) = -cos α

tan (180° - α) = -tan α

cotan (180° - α) = -cotan α

secan (180° - α) = secan α

sec (180° - α) = -sec α

Kuadran III : 180° < α < 270° (π < α < 3π/2)

sin (270° - α) = -cos α

cos (270° - α) = -sin α

tan (270° - α) = cotan α

cotan (270° - α) = tan α

secan (270° - α) = -sec α

sec (270° - α) = -cosec α

Kuadran IV : 270° < α < 360° (3π/2 < α < 2π)

sin (360° - α) = sin (-α) = -sin α

cos (360° - α) = cos (-α) = cos α

tan (360° - α) = tan (-α) = -tan α

cotan (360° - α) = cotan (-α) = -cotan α

secan (360° - α) = secan (-α) = -secan α

sec (360° - α) = sec (-α) = sec α

Kemudian, nilai-nilai sudut istimewa, yaitu :

sin 30° = 1/2, cos 30° = 1/2 √3, tan 30° = 1/3 √3

sin 45° = 1/2 √2, cos 45° = 1/2 √2, tan 45° = 1

sin 60° = 1/2 √3, cos 60° = 1/2, tan 60° = √3

sin 90° = 1, cos 90° = 0, tan 90° = ∞

Mari kita lihat soal berikut.

tan 150° berada pada kuadran II, sehingga nilai tangen negatif.

tan 150°

= tan (180 - 30)°

= -tan 30°

= \begin{gathered} -\frac{sin30^o}{cos30^o}\\= -\frac{ \frac{1}{2}} { \frac{1}{2} \sqrt{3} }\\=- \frac{1}{ \sqrt{3} }\\=- \frac{1}{3} \sqrt{3} \end{gathered}

−

cos30

o

sin30

o

=−

2

1

3

2

1

=−

3

1

=−

3

1

3