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Math Help - Find the indicated trigonometric function given that...

  1. #1
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    Question Find the indicated trigonometric function given that...

    ... (theta) is an angle in standard position with the terminal side passing through the given point.

    (-7,-3); Find sec(theta).

    (15,20); Find csc(theta).

    (6,-8); Find cot(theta).



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  2. #2
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    Re: Find the indicated trigonometric function given that...

    Hello, MaddyV!

    I'll do the first one . . .


    \theta is an angle in standard position with the terminal side passing through the given point.

    . . (\text{-}7,\text{-}3);\;\text{ Find }\sec\theta

    We are given: . \begin{Bmatrix}x &=& \text{-}7 \\ y &=& \text{-}3 \end{Bmatrix}

    . . and: . r \:=\:\sqrt{x^2+y^2} \:=\:\sqrt{(\text{-}7)^2 + (\text{-}3)^2} \:=\:\sqrt{58}

    Then we have these definitions: . \begin{Bmatrix}\sin\theta \:=\:\dfrac{y}{r} && \csc\theta \:=\:\dfrac{r}{y} \\ \\[-3mm] \cos\theta \:=\:\dfrac{x}{r} && \sec\theta \:=\:\dfrac{r}{x} \\ \\[-3mm] \tan\theta \:=\:\dfrac{y}{x} && \cot\theta \:=\:\dfrac{x}{y} \end{Bmatrix}

    Can you finish the problem now?
    Thanks from MaddyV
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  3. #3
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    Re: Find the indicated trigonometric function given that...

    (square root)58/-7 ! Yes! Thank you so much!
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