Suppose that cos(x) = -4/5, and pi/2 < x < pi. Find the exact value of cos(2x). (Enter an exact number as an integer, fraction, or decimal.)

Question

I am really struggling with this portion of my homework. Help would be greatly appreciated, thank you.

Answer 1

Note that cos(2x)=cos(x+x)=cosxcosx-sinxsinx. If cosx = -4/5 then sinx = sqrt(5²-4²)/5=3/5 (use right triangle and pythagoras theorem). Now find that cos(2x)=(-4/5)²-(3/5)²=7/25. Note that 2x is in the IV quadrant.