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Simplify: arcsin (sin x), pi/2 <= x <=pi?

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  • 10 years ago
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    This is an exercise in the default ranges for the functions.

    x is in the second quadrant; its sin will be positive.

    If you take the arcsin of that, you obviously get the reference angle (first quadrant).

    What relationship does that have with its "sibling" angle in the 2nd quadrant?

    That's what the problem wants you to think about.

    That can be restated as ...

    A quadrant II angle, x, has a sine of "a".

    A quadrant I angle, y, also has a sine of "a".

    What's the relationship between x and y?

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