the answer has to be in both radians and degrees
2006-09-04 11:19:18 · 4 answers · asked by da_1_n_only 1 in Education & Reference ➔ Homework Help
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.
2006-09-04 11:40:39 · answer #1 · answered by alrivera_1 4 · 0⤊ 0⤋
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!
2006-09-04 18:27:02 · answer #2 · answered by Anonymous · 0⤊ 0⤋
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.
2006-09-04 18:28:05 · answer #3 · answered by lemons 3 · 0⤊ 0⤋
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
2006-09-04 18:23:50 · answer #4 · answered by raj 7 · 0⤊ 0⤋