How would you find the exact value? Cos(2arccos(5/7)) using double angle formula

Question

mathmale · Answer

Sara:  I don't see any "theta" in this problem statement.    Please correct your statement and resubmit it here.

saraa23 · Answer

I fixed the question. I added the theta on accident to the question

anonymous · Answer

$\cos(2 \theta) = 2\cos^{2} (\theta) - 1$ 
Let your "theta" be equal to $\arccos (5/7)$ and plug in.

saraa23 · Answer

I am getting -48/49, and it is coming out to be wrong. I don't know where I'm going wrong

danjs · Answer

2 * [ cos( cos^-1( 5/7 )) ] ^2  - 1

danjs · Answer

that is   1/49  if that works

danjs · Answer

cos[ cos^-1(x)]  ---> x    ,  a function and inverse remove each other

danjs · Answer

2*[5/7]^2  - 1

2* (25/49) - 1

1/49

saraa23 · Answer

Okay now I see why cos and cos^1 cancel out ! Makes so much more sense thank you !

danjs · Answer

i think you figured (5/7)^2 - 1,   then doubled that,  operation order little off

danjs · Answer

need 2*[5/7]^2 first , then take the 1 off

saraa23 · Answer

Yess that's what I did. I see my mistake now.

danjs · Answer

k, welcome