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
- alrivera_1Lv 41 decade agoFavorite Answer
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
- Anonymous1 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!
- 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.
- rajLv 71 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