Given that sin 𝐴=513 and 0∘≤𝐴≤360∘ , what are all possible values of cos A ?

To find the possible values of cos A, we need to use the Pythagorean identity for sine and cosine, which is sin²A + cos²A = 1.

Given that sin A = 5/13, we can substitute this into the Pythagorean identity:

(5/13)² + cos²A = 1 25/169 + cos²A = 1 cos²A = 1 - 25/169 cos²A = 144/169

Taking the square root of both sides gives two possible solutions, cos A = ±12/13.

However, we need to consider the quadrant in which angle A lies. Since sin A is positive and 0° ≤ A ≤ 360°, A could be in the first or second quadrant.

In the first quadrant, both sine and cosine are positive, so cos A = 12/13.

In the second quadrant, sine is positive and cosine is negative, so cos A = -12/13.

So, the possible values of cos A are 12/13 and -12/13.