Question

What does Cos a/2 equal to?

Answer 1

cos(α2)= −1/5√2

Explanation:

you are given tan(α)=7/24 , so you can find the length of the hypotenuse using the Pythagorean theorem, which is a2+b2=c2 with a and b being the legs of the triangle and c being the hypotenuse of the triangle.

c2=7^2+24^2

⟹c2=49+576

⟹c2=625

⟹c=25

if π<α<3π/2 , then α has to lie in quadrant III where cosine is negative. so cos(α)= −24/25

The half-angle identity for the cosine function is cos(α2)=±√1+cos(α)/2 , so plugging the information in, we get

cos(α2)=±√ 1+(−24/25)/2

⟹ cos(α2)=±√1/25 / 2

⟹cos(α2)=±√1/50

⟹cos(α2)=±1/5√2