Question

Use the given information to find the exact value of the expression. sin θ = 24/25, θ lies in quadrant II Find tan 2θ. A. - 526/527 B.336/625 C. -336/527 D. 336/527

Answer 1

Because θ lies in quadrant II, 2θ must lie in quadrant IV. This means the tangent of 2θ is negative.
The adjacent side to θ is 7 because √(25²-24²)=7, so tanθ=7/24.
The double angle formula for tangent is tan 2θ = (2 tan θ) / (1 − tan² θ).
Substituting the value for tanθ in and keeping in mind that this is in quadrant IV, we get tan 2θ = -(2(7/24)/(1-(7/24)²)). 
Simplified, this becomes tan 2θ = -336/527. 
Therefore, the answer is C. -336/527.