Trigonometry is weird...

Question

 for 

then:

sin(x/2)=?

cos(x/2)=?

tan(x/2)=?

My math teacher explained how to do this very poorly, help me, please.

Answer 1

two methods

Method 1: solve for x, divide by 2, use a calculator

sin(x) = 1/cscx = 1/2 in Quad 2, x= 150

x=150,

x/2 = 75

sin(x/2) = sin75 = about 0.966

cos(x/2) = cos75 = 0.259

tan(x/2) = tan75 = 3.732

Method 2: use the half angle formulas

sinx/2 = sqr((1-cosx)/2) = sqr(1+sqr3/2)/2)= 0.966

cosx/2 =sqr((1+cosx)/2) =sqr(1-sqr3/2)/2) =0.259

tanx/2 =sqr((1-cosx)/(1+cosx) = sqr(1.866/0.134) = 3.732