Final answer:
To find cosA using the half-angle formula for cosine, we can substitute the given value of cos2A and apply the formula. By determining the quadrant of 2A and considering the sign of cosine, we can find the value of cosA as -sqrt(11/18).
Step-by-step explanation:
To find cosA, we will use the half-angle formula for cosine:
cos(A/2) = sqrt((1+cosA)/2)
Given that cos2A = 2/9, we can rewrite it as:
cos(A/2) = sqrt((1+2/9)/2)
cos(A/2) = sqrt(11/18)
Since 2A is in the Fourth Quadrant, A/2 will also be in the Fourth Quadrant. In the Fourth Quadrant, cosine is negative. Therefore, cos(A/2) is negative.
Therefore, cosA = -sqrt(11/18).