Question

What is the exact value of sin(157.5°)?

Answer 1

Answer:

$\frac{\sqrt{2 - \sqrt{2} } }{2}$

Step-by-step explanation:

$sin ^{2}$  $(157.5°)$  $=$  $1/2(1 - cos(2*157.5))$

$==> 1/2(1 - cos(315))$

$==> 1/2(\sqrt{2} /2)$

$==> (2 - \sqrt{2} ) / 4$

sin(157.5°)  is in quadrant ll , meaning sin(157.5°) is greater than 0 , so we take positive square root of sin(157.5°)

sin(157.5) = $\frac{\sqrt{2 - \sqrt{2} } }{2}$