Find the values of the following trigonometric ratios: sin (151π )/6

Question

Find the values of the following trigonometric ratios:

sin \(\cfrac{151\pi}6\)

Answer 1

Given sin \(\cfrac{151\pi}6\)

⇒ sin \(\cfrac{151\pi}6\) = sin 4530°

⇒ sin 4530° = 90° × 50 + 30°

4530° lies in the third quadrant in which the sine function is negative.

∴ sin 4530° = sin (90° × 50 + 30°)

= - sin 30°

= -1/2