cosA= 5/9 find cos1/2A
are you familiar with the half-angle formulas?
the one I would use here is
cos A = 2cos^2 (1/2)A - 1
5/9 + 1 =2cos^2 (1/2)A
14/9 =2cos^2 (1/2)A
cos (1/2)A = √(7)/3
Yes, I am familiar with the half-angle formulas. In this case, we can use the half-angle formula for cosine to find cos(1/2)A. The formula states that cos(A) = 2cos^2(1/2)A - 1.
To solve for cos(1/2)A, we can rearrange the formula and substitute the given value of cosA:
cosA = 5/9
5/9 = 2cos^2(1/2)A - 1
To isolate cos^2(1/2)A, we can add 1 to both sides of the equation:
5/9 + 1 = 2cos^2(1/2)A
14/9 = 2cos^2(1/2)A
Now, we can solve for cos^2(1/2)A by dividing both sides of the equation by 2:
14/9 / 2 = cos^2(1/2)A
7/9 = cos^2(1/2)A
Finally, to find cos(1/2)A, we can take the square root of both sides of the equation:
√(7/9) = cos(1/2)A
Simplifying the square root gives:
√(7/9) = √7/√9 = √7/3
Therefore, cos(1/2)A = √7/3.