Question 1064475
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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}}}

the answer is {{{15pi / 4}}} but I got only {{{7pi/4}}} What did I do wrong?
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You correctly determined that {{{sin(2theta)}}} = {{{sqrt(2)/2}}}.

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


Hence, {{{theta}}} lies in QI.


Therefore {{{2theta)}}} can be one of the two angles: {{{pi/4}}} or {{{3pi/4}}} and CAN NOT be anything different.


Moreover, since  {{{sin(theta)}}} < {{{cos(theta)}}}, the angle {{{theta}}} is less than {{{pi/4}}}.


Therefore, {{{2theta}}} = {{{pi/4}}} and CAN NOT be anything different.
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