If cosθ = 3/7 with 0<θ<π/2, find tanθ

Answer 1

1. Draw an appropriate triangle.

This is in quadrant 1 (0 < θ < π/2) so, since cosine = adjacent/hypotenuse:

2. Using the Pythagorean Theorem, solve for the opposite side:

3² + (opp)² = 7²

(opp)² = 49 - 9 = 40

opp = √40 = 2√10

3. Use the opposite side you calculated to find tan(θ)

tan(θ) = opp/adj = 2√10/3