What does Cos a/2 equal to?

cos(α2)= −1/5√2

Step-by-step 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