parabola Given that tanθ= -\frac{9}{4} and \frac{\pi }{2\\}<θ<π , find the exact values of the trigonometr

Question

parabola
Given that tanθ= -\frac{9}{4} and \frac{\pi }{2\\}<θ<π , find the exact values of the trigonometric functions.

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RobertKer 3 years 2021-08-14T20:13:26+00:00 1 Answers 9 views 0

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  1. Philomena
    0
    2021-08-14T20:15:00+00:00
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    9514 1404 393

    Answer:

    • sin(θ) = (9√97)/97
    • cos(θ) = (-4√97)/97
    • csc(θ) = (√97)/9
    • sec(θ) = (-√97)/4
    • cot(θ) = -4/9

    Step-by-step explanation:

    The angle is in the 2nd quadrant, where the sine is positive and the cosine is negative.

    tan^2(θ) +1 = sec^2(θ) = (-9/4)^2 +1 = 97/16   ⇒   sec = -(1/4)√97

    cot(θ) = 1/tan(θ) = -4/9

    csc^2(θ) = cot^2(θ) +1 = (-4/9)^2 +1 = 97/81   ⇒   csc = (1/9)√97

    sin(θ) = 1/csc(θ) = (9√97)/97

    cos(θ) = 1/sec(θ) = (-4√97)/97

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