Question

Find the exact value of sin 165º.

Answer 1

Answer:0.2588

Step-by-step explanation:

Answer 2

Answer:

$\frac{1}{4}$ ( $\sqrt{6}$ - $\sqrt{2}$ )

Step-by-step explanation:

Using the sine addition formula

sin(a + b) = sinacosb + cosasinb

and the exact values

sin45° = cos45° = $\frac{\sqrt{2} }{2}$ , sin60° = $\frac{\sqrt{3} }{2}$ , cos60° = $\frac{1}{2}$

Given

sin165°

Note that 165° = (120 + 45)°, thus

= sin(120 + 45)°

= sin120°cos45° + cos120°sin45°

= sin60°cos45° - cos60°sin45°

= ( $\frac{\sqrt{3} }{2}$ × $\frac{\sqrt{2} }{2}$ ) - ( $\frac{1}{2}$ × $\frac{\sqrt{2} }{2}$ )

= $\frac{\sqrt{6} }{4}$ - $\frac{\sqrt{2} }{4}$

= $\frac{1}{4}$ ( $\sqrt{6}$ - $\sqrt{2}$ )