Thread: trig find value

Find the exact values for the following:


cos(4*cos^-1(1/3))

cosine of ( four times the inverse cosine of (1/3) )


what I wrote above are the same, I just wanted to spell them out just in case.

Originally Posted by Mr_Green

Find the exact values for the following:


cos(4*cos^-1(1/3))

cosine of ( four times the inverse cosine of (1/3) )


what I wrote above are the same, I just wanted to spell them out just in case.

cos(4t) = cos(2*(2t)) = 2*cos^2(2t) - 1 = 2*[2*cos^2(t) - 1]^2 - 1

Let t = cos^{-1}(1/3).

Then
cos(4*cos^{-1}(1/3)) = 2*[2*cos^2(cos^{-1}(1/3)) - 1]^2 - 1

= 2*[2*(1/3)^2 - 1]^2 - 1

= 2*[2/9 - 1]^2 - 1

= 2*[-7/9]^2 - 1

= 2*49/81 - 1

= 98/81 - 1

= 17/81

-Dan