Question

How do you find the value of `sin (157 1/2)`?

Answer 1

`sqrt((sqrt 2-1)/(2sqrt2))`=0.3827, nearly.

Explanation:

`167.5^o` is angle in the 2nd quadrant. So, sin is positive.

`Also, sin 157.5^o=sin (180^0-157.5^o)=sin 22.5^o`

Now, use `cos 2t = (1-2sin^2 t)`

`cos 45^o=1/sqrt 2=(1-2 sin^2 22.5^o)`

Solving for positive root,

`sin 22.5^o=sqrt((1-1/sqrt 2)/2)`