Step 1: Start with the given value of sin A, which is 3/5.
Step 2: Use the Pythagorean identity, which states that sin^2 A + cos^2 A = 1.
Step 3: Calculate sin^2 A by squaring 3/5. This gives (3/5)^2 = 9/25.
Step 4: Substitute sin^2 A into the identity: 9/25 + cos^2 A = 1.
Step 5: To find cos^2 A, rearrange the equation: cos^2 A = 1 - 9/25.
Step 6: Convert 1 into a fraction with a denominator of 25: 1 = 25/25.
Step 7: Now subtract: cos^2 A = 25/25 - 9/25 = 16/25.
Step 8: To find cos A, take the square root of cos^2 A: cos A = sqrt(16/25).
Step 9: Calculate the square root: cos A = 4/5.
Trigonometric Identities – Understanding and applying the Pythagorean identity sin^2 A + cos^2 A = 1 to find the cosine of an angle when the sine is known.
