How do you use the half angle formulas to determine the exact values of sine, cosine, and tangent of the angle $112^circ 30'$ ?

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Answer 1 · 2017-02-11T17:22:18

See explanation.

$sin(112^o30')=sin(90+22.5)^o=cos22.5^o$

$=sqrt(1/2(1+cos45^o))=sqrt(1/2(1+1/sqrt2))$ .

Likewise,

$cos(112^o30')=cos(90+22.5)^o=-sin22.5^o$

$=-sqrt(1/2(1-cos45^o))$

$=-sqrt(1/2(1-1/sqrt2))$ .

$tan(112.5^o=tan(90+22.5)^o=-cot22,5^$

$=-(cos22.5^o)/(sin22.5^o)=-sqrt((sqrt2+1)/(sqrt2-1))$

How do you use the half angle formulas to determine the exact values of sine, cosine, and tangent of the angle 112^circ 30'112^circ 30'?