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Suppose that Sin(θ)=5/13 and cos(θ)=-12/13. Find the value of tan(θ), cot (θ), CSC (θ), and sec (θ). Find the value of tan(2θ)
I know the values are tanθ=5/12, cscθ=13/5, secθ=13/-12 and cotθ=-12/5 but I don't know how to find tan(2θ)

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ciallen21

Answer:

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.

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