SOLUTION: If {{{cos(theta) = sqrt( 1/2 + 1/(2 * sqrt( 2 ))) }}} and {{{sin(theta) = sqrt( 1/2 - 1/(2 * sqrt( 2 ))) }}} with {{{0 <= theta < 2pi}}} it follows that {{{2theta}}} = .... {{{pi}

Algebra ->  Trigonometry-basics -> SOLUTION: If {{{cos(theta) = sqrt( 1/2 + 1/(2 * sqrt( 2 ))) }}} and {{{sin(theta) = sqrt( 1/2 - 1/(2 * sqrt( 2 ))) }}} with {{{0 <= theta < 2pi}}} it follows that {{{2theta}}} = .... {{{pi}      Log On


   

Question 1064475: If cos%28theta%29+=+sqrt%28+1%2F2+%2B+1%2F%282+%2A+sqrt%28+2+%29%29%29+ and sin%28theta%29+=+sqrt%28+1%2F2+-+1%2F%282+%2A+sqrt%28+2+%29%29%29+ with 0+%3C=+theta+%3C+2pi it follows that 2theta = .... pi
the answer is 15pi+%2F+4 but I got only 7pi%2F4 What did I do wrong?
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
If cos%28theta%29+=+sqrt%28+1%2F2+%2B+1%2F%282+%2A+sqrt%28+2+%29%29%29+ and sin%28theta%29+=+sqrt%28+1%2F2+-+1%2F%282+%2A+sqrt%28+2+%29%29%29+ with 0+%3C=+theta+%3C+2pi it follows that 2theta = .... pi
the answer is 15pi+%2F+4 but I got only 7pi%2F4 What did I do wrong?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

You correctly determined that sin%282theta%29 = sqrt%282%29%2F2.

Notice that both sin%28theta%29 and cos%28theta%29 are positive, as it is (implicitly) stated by the condition.


Hence, theta lies in QI.


Therefore 2theta%29 can be one of the two angles: pi%2F4 or 3pi%2F4 and CAN NOT be anything different.


Moreover, since  sin%28theta%29 < cos%28theta%29, the angle theta is less than pi%2F4.


Therefore, 2theta = pi%2F4 and CAN NOT be anything different.