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# Trigonometric Double-Angle and Half-Angle Formulas?

cos θ = 5/13, with θ being in Quadrant I

How do i find tan 2θ?

also,

If sin θ = −5/13 and θ is in Quadrant III

How do i find find tan(θ/2)?

### 1 Answer

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- 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)

= 120/119

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)

= -5

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