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

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Answer 1 · 2016-06-30T14:27:53

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

$167.5^o$ 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,

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

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