a.sin 130° = 0,766

b.sin 200° = - 0,342

c.tan 250° = 2,748

d.sin 290° = - 0,940

e.cos 323° = 0,799

f.sec 150° = - 2/3 √3

g.coses 170° = 5,747

h.cot 30° = √3

i.sec 300° = 2

j.cot 255° = \frac{1 - \frac{1}{3}\sqrt{3}}{1 + \frac{1}{3}\sqrt{3}}

Pembahasan

Untuk mengerjakan soal itu semua kita akan menggunakan berbagai rumus perbandingan trigonometri kuadran lain dengan relasi pada kuadran 1

Rumusnya adalah

Kuadran 2

Sin (180° - α) = Sin α

Cos (180° - α) = - Cos α

Tan (180° - α) = - Tan α

Kuadran 3

Sin (180° + α) = - Sin α

Cos (180° + α) = - Cos α

Tan (180° + α) = Tan α

Kuadran 4

Sin (360° - α) = - Sin α

Cos (360° - α) = Cos α

Tan (360° - α) = - Tan α

Penyelesaian

a. Sin 130° ⇒ (130° = 180° - 50°)

Sin 130° = Sin (180° - 50°) = Sin 50° = 0,766

b. Sin 200° ⇒ (200° = 180° + 20°)

Sin 200° = Sin (180° + 20°) = - Sin 20° = - 0,342

c. Tan 250° ⇒ (250° = 180° + 70°)

Tan 250° = Tan (180° + 70°) = Tan 70° = 2,748

d. Sin 290° ⇒ (290° = 360° - 70°)

Sin 290° = Sin (360° - 70°) = - Sin 70° = - 0,940

e. Cos 323° ⇒ (323° = 360° - 37°)

Cos 323° = Cos (360° - 37°) = Cos 37° = 0,799

f. Sec 150° = 1/cos 150°

Cos 150° ⇒ (150° = 180° - 30°)

Cos 150° = Cos (180° - 30°) = - Cos 30° = -1/2 √3

Sec 150° = 1/ -1/2 √3 = -2/3 √3

g. Cosec 170° = 1/Sin 170°

Sin 170° ⇒ (170° = 180° - 10°)

Sin 170° = Sin (180° - 10°) = Sin 10° = 0,174

Cosec 170° = 1/0,174 = 5,747

h. Cot 30° = 1/Tan 30° = 1/1/3 √3 = √3

i. Sec 300° = 1/Cos 300°

Cos 300° ⇒ (300° = 360° - 60°)

Cos 300° = Cos (360° - 60°) = Cos 60° = 1/2

Sec 300° = 1/ 1/2 = 2

j. Cot 255° = 1/Tan 255°

Tan 255° ⇒ (180° + 75°)

Tan 255° = Tan (180° + 75°)

Tan 255° = Tan 75°

Tan 255° = Tan (45° + 30°)

Tan 255° = \frac{Tan 45^o + Tan 30^o}{1 - Tan 45^o \times Tan30^o}

Tan 255° = \frac{1 + \frac{1}{3}\sqrt{3}}{1 - 1 \times \frac{1}{3}\sqrt{3}}

Tan 255° = \frac{1 + \frac{1}{3}\sqrt{3}}{1 - \frac{1}{3}\sqrt{3}}

Cot 255° = 1/Tan 255° = \frac{1 - \frac{1}{3}\sqrt{3}}{1 + \frac{1}{3}\sqrt{3}}