Let θ = sin^(-1)(3/5). Then sin(θ) = 3/5 and using the Pythagorean theorem, cos(θ) = 4/5. Therefore, tan(θ) = sin(θ)/cos(θ) = (3/5)/(4/5) = 3/4.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate tan(sin^(-1)(3/5)).
Solution: Let θ = sin^(-1)(3/5). Then sin(θ) = 3/5 and using the Pythagorean theorem, cos(θ) = 4/5. Therefore, tan(θ) = sin(θ)/cos(θ) = (3/5)/(4/5) = 3/4.
Steps: 9
Step 1: Let θ = sin^(-1)(3/5). This means that sin(θ) = 3/5.
Step 2: To find cos(θ), use the Pythagorean theorem. We know that sin^2(θ) + cos^2(θ) = 1.
Step 3: Calculate sin^2(θ): (3/5)^2 = 9/25.
Step 4: Substitute sin^2(θ) into the Pythagorean theorem: 9/25 + cos^2(θ) = 1.
