Question

given tan A = 7/√120 and that angle A is in Quadrant III, find the exact value of cos A in simplest radical form using a rational denominator.

Answer 1

Explanation:

Step 1: We know that the cosine of an angle in Quadrant III is negative.

Step 2: We convert the given angle A into radians by multiplying it by pi/180.

A = (7/√120) * (π/180) = (7π)/(12√5)

Step 3: We use the cosine formula to find the exact value of cos A.

cos A = cos((7π)/(12√5))

Step 4: We simplify the result using trigonometric identities.

cos A = (-1/3)√5