Given sin θ = -3/5 and csc θ = -5/3 in quadrant III, find the value of other trigonometric functions using a Pythagorean Identity. Show your

Question

Given sin θ = -3/5 and csc θ = -5/3 in quadrant III, find the value of other trigonometric functions using a Pythagorean Identity. Show your work.

Part I: Find the value of cos θ and sec θ

Part II: Using your answers from Part I, find the value of tan θ

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Clara 2 weeks 2021-10-11T19:52:55+00:00 2 Answers 0

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    0
    2021-10-11T19:54:31+00:00

    I. Since \theta lies in quadrant 3, we know \cos\theta<0. The Pythagorean identity tells us

    \cos^2\theta+\sin^2\theta=1\implies\cos\theta=-\sqrt{1-\sin^2\theta}=\boxed{-\dfrac45}

    \implies\sec\theta=\dfrac1{\cos\theta}=\boxed{-\dfrac54}

    II. By definition of tangent,

    \tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{-\frac35}{-\frac45}=\boxed{\dfrac34}

    0
    2021-10-11T19:54:37+00:00

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