Trigonometric Double-Angle and Half-Angle Formulas?
cos θ = 5/13, with θ being in Quadrant I
How do i find tan 2θ?
If sin θ = −5/13 and θ is in Quadrant III
How do i find find tan(θ/2)?
- Kathleen KLv 77 years agoFavorite Answer
If θ terminates in Q I and has cosine of 5/13, then tan θ = 5/12 (draw a right triangle or use the Pythagorean identities). The double angle formula for tangent is:
tan 2θ = 2tanθ / (1-tan²θ)
= 2(5/12) / (1-(5/12)²)
= (5/6) / (119/144)
If θ terminates in Q III and sinθ = -5/13, then cosθ = -12/13. The half angle formula for tangent is:
tan (θ/2) = sinθ/(1+cosθ)
= (-5/13) / (1-12/13)
= (-5/13) / (1/13)