Yahoo Answers: Answers and Comments for Can somebody help me solve this problem but tell me how to do it step by step: sin1 square root of 2/2? [Homework Help]
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From da_1_n_only
enUS
Mon, 04 Sep 2006 15:19:18 +0000
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Yahoo Answers: Answers and Comments for Can somebody help me solve this problem but tell me how to do it step by step: sin1 square root of 2/2? [Homework Help]
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From alrivera_1: Ok, this is a simple problem once you visualiz...
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Mon, 04 Sep 2006 22:40:39 +0000
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.

From lemons: you have to know the value of the sine and cos...
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Mon, 04 Sep 2006 22:28:05 +0000
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.

From Anonymous: Straight off of the unit circle. Look to see ...
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Mon, 04 Sep 2006 22:27:02 +0000
Straight off of the unit circle. Look to see where the ycoordinate 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!

From raj: sin^1(rt2/2) is the same as sin^1(1/rt2)
th...
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Mon, 04 Sep 2006 22:23:50 +0000
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