Question

Find the exact value of the expression. cos(tan^(-1) sqrt(3)/3)

Answer 1

to solve this, we need to express cosine in terms of tangent, since we know how to compute tan(arctan(x)). let's use some identities:

tan(x)=sin(x)/cos(x)=sqrt(1-cos(x)^2)/cos(x)
tan(x)^2=(1-cos(x)^2)/cos(x)^2=1/cos(x)^2-1
tan(x)^2+1=sec(x)^2
cos(x)=sqrt(1/(tan(x)^2+1)).

thus cos(arctan(sqrt(3)/3)) = sqrt(1/((sqrt(3)/3)^2+1))

Answer 2

my solution choices are sqrt(3)/3; 1/2; pi/3; or sqrt(3)/2 when I was working it out I was getting 1/2 but it just didn't seem correct.

Answer 3

the answer should be sqrt(3)/2. it might help to use 1/sqrt(3) instead of sqrt(3)/3 in the equation.

Answer 4

Thank you, I just can't seem to get a handle on trig identities!!!