If sin θ = 3/5 and cos θ > 0, what is cos θ?

• A. 4/5
• B. 3/5
• C. -4/5
• D. -3/5

Answer: (A)

This question tests how sine and cosine are linked by the Pythagorean identity and how the sign of cosine is determined by the quadrant. Using sin^2 θ + cos^2 θ = 1, substitute sin θ = 3/5 to get sin^2 θ = 9/25, so cos^2 θ = 1 − 9/25 = 16/25. Thus |cos θ| = 4/5. The condition cos θ > 0 tells us to take the positive value, giving cos θ = 4/5. Also, since sin θ is positive and cos θ is positive, θ lies in the first quadrant, where both functions are positive, which aligns with cos θ = 4/5.