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

Question

6504 views around the world

You can reuse this answer
Creative Commons License

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))#