Find $\cos (2 A)$, if $\cos (A)=-\frac{21}{29}$, and $A$ is in quadrant 3 Submit Question

Step 1 ：We are given that \(\cos(A) = -\frac{21}{29}\) and that \(A\) is in quadrant 3.

Step 2 ：We are asked to find \(\cos(2A)\).

Step 3 ：We know that the formula for \(\cos(2A)\) is \(2\cos^2(A) - 1\).

Step 4 ：Substituting \(\cos(A) = -\frac{21}{29}\) into the formula, we get \(\cos(2A) = 2(-\frac{21}{29})^2 - 1\).

Step 5 ：Solving this, we find that \(\cos(2A) = 0.04875148632580273\).

Step 6 ：Since \(A\) is in quadrant 3, \(\cos(2A)\) will also be negative.

Step 7 ：So, the final answer is \(\boxed{0.04875148632580273}\).