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can somebody help me solve this problem but tell me how to do it step by step: sin-1 square root of 2/2?

the answer has to be in both radians and degrees

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  • 1 decade ago
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    Ok, this is a simple problem once you visualize it.

    1. Draw a right triangle with sides equal to 1.

    2. The hypotenuse is given by sqrt (2)

    3. Define angles A and B (both are 45 by definition, but we will prove it).

    4. sin (A) = opposite / hypotenuse = 1/sqrt(2)

    5. Multiplying 1/sqrt(2) by (sqrt(2)/sqrt(2)) the above result

    6. sin(A) = sqrt(2)/2

    From Math tables or your calculator you can find that inverse sin(sqrt(2)/2)) is 45 degrees (from your triangle you knew that).

    7. Converting 45 degrees to radians

    45 * (pi/180) = pi/4

    Good luck.

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  • Anonymous
    1 decade ago

    Straight off of the unit circle. Look to see where the y-coordinate matches -square root of 2 over 2. That would be at 5pi over 4 and 7pi over 4 or 225 and 315 degrees. I teach trig!

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  • 1 decade ago

    you have to know the value of the sine and cosine of 'simple' angles. this knowledge is crucial.

    at any rate, the value of sine 2^1/2 / 2 = 45 degrees, or pi/4. there's not too many steps to it but you really have to memorize the values of sine and cosine for 0, 30, 35, 60 and 90 degrees.

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  • raj
    Lv 7
    1 decade ago

    sin^-1(rt2/2) is the same as sin^-1(1/rt2)

    this means that angle whose sine ratiois 1/rt2

    you know that sin 45* or sin pi/4 is 1/rt2

    therefore sin^-1(rt2/2)=45* or pi/4

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