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}}
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