Question

If sin θ = 5/13 and θ is an acute angle, find cos θ and tan θ.

Solution

1. Use sin^2 θ + cos^2 θ = 1: cos^2 θ = 1 - (5/13)^2 = 1 - 25/169 = 144/169.
2. Since θ is acute, cos θ is positive, so cos θ = 12/13.
3. tan θ = sin θ / cos θ = (5/13) / (12/13) = 5/12.
4. Check: the sides 5, 12, and 13 form a right triangle.