Find the values of the following trigonometric ratios: sin(41π/4)

Question

Find the values of the following trigonometric ratios:

sin(\(\cfrac{41\pi}4\))

Answer 1

Given sin(\(\cfrac{41\pi}4\))

⇒ sin(\(\cfrac{41\pi}4\)) = sin 1845°

⇒ sin 1845° = 90° × 20 + 45°

1845° lies in the first quadrant in which the sine function is positive.

∴ sin 1845° = sin (90° × 20 + 45°)

= sin 45°

= \(\cfrac1{\sqrt2}\)