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Math Help - Inverse Trigonometric Functions

  1. #1
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    Inverse Trigonometric Functions

    Note:
     arcsin(siny) \neq y if y is not in the interval [-1,1]

    Question:
     arcsin(sin\frac{3\pi}{4})            \neq \frac{3\pi}{4}

    Why ?

    Attempt:
    I try doing it with the calculator but i keep getting \frac{3\pi}{4}




    thank you
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  2. #2
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    Quote Originally Posted by mj.alawami View Post
    Note:
     arcsin(siny) \neq y if y is not in the interval [-1,1]

    Question:
     arcsin(sin\frac{3\pi}{4}) \neq \frac{3\pi}{4}

    Why ?

    Attempt:
    I try doing it with the calculator but i keep getting \frac{3\pi}{4}

    thank you
    \frac{3\pi}{4} \approx \frac{3 \times 3.14159}{4}.

    What does this equal? Is it in the interval [-1, 1]?
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  3. #3
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    Quote Originally Posted by mj.alawami View Post
    Note:
     arcsin(siny) \neq y if y is not in the interval [-1,1] Mr F says: This interval is wrong. It should be {\color{red}\left[ -\frac{\pi}{2}, \frac{\pi}{2}\right]}.

    Question:
     arcsin(sin\frac{3\pi}{4}) \neq \frac{3\pi}{4}

    Why ?

    Attempt:
    I try doing it with the calculator but i keep getting \frac{3\pi}{4}

    thank you
    \sin \frac{3 \pi}{4} = \frac{1}{\sqrt{2}}.

    \arcsin \frac{1}{\sqrt{2}} = \frac{\pi}{4} since the range of the arcsin function is, by definition, \left[ -\frac{\pi}{2}, \frac{\pi}{2}\right].
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