SOLUTION: Hi there, I'm having trouble understanding how to go about solving this question; after looking through various examples it still doesn't seem to make any sense to me, so some h

Algebra ->  Trigonometry-basics -> SOLUTION: Hi there, I'm having trouble understanding how to go about solving this question; after looking through various examples it still doesn't seem to make any sense to me, so some h      Log On


   

Question 1065109: Hi there,
I'm having trouble understanding how to go about solving this question; after looking through various examples it still doesn't seem to make any sense to me, so some help would be much appreciated!
Find all the solutions between -2pi and 2pi of the equation:
sin(theta)=1/sqrt(2)
Give all of your answers as exact values in radians
Thank you very much!
Found 2 solutions by MathTherapy, ikleyn:
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
I'm having trouble understanding how to go about solving this question; after looking through various examples it still doesn't seem to make any sense to me, so some help would be much appreciated!
Find all the solutions between -2pi and 2pi of the equation:
sin(theta)=1/sqrt(2)
Give all of your answers as exact values in radians
Thank you very much!
sin+%28theta%29+=+1%2Fsqrt%282%29

sin+%28theta%29+=+1%2Fsqrt%282%29+%2A+sqrt%282%29%2Fsqrt%282%29 ------ RATIONALIZING denominator

sin+%28theta%29+=+sqrt%282%29%2F2, which is: 

sin is positive (+), so the angles are in the 1st and 2nd quadrants only!

If you still don't understand, then consult the UNIT CIRCLE.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
Corrections to the solution by "MathTherapy" 

sin+%28theta%29+=+1%2Fsqrt%282%29
sin+%28theta%29+=+1%2Fsqrt%282%29+%2A+sqrt%282%29%2Fsqrt%282%29 ------ RATIONALIZING denominator
sin+%28theta%29+=+sqrt%282%29%2F2, which is: 


All these angles are in 1-st and the 2-nd quadrant.

No positive sine in the 3-rd and 4-th quadrant.