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

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Mathematics

Oprah

30 July, 17:57

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

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Zamora · 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.