Question 825697
I need help with this problem... Solve the equation sqrt(2) sinx=1 on the interval [0,2π). Write your answer in terms of π.



sqrt(2)*sinx=1


sinx = 1/sqrt(2)


sinx = sqrt(2)/2 ... rationalize the denominator


x = arcsin(sqrt(2)/2) ... take the arcsine of both sides


x = pi/4 or x = 3pi/4 ... use the unit circle (link: <a href="http://www.regentsprep.org/Regents/math/algtrig/ATT5/600px-Unit_circle_angles_svg.jpg">http://www.regentsprep.org/Regents/math/algtrig/ATT5/600px-Unit_circle_angles_svg.jpg</a>)


The two solutions are {{{x = pi/4}}} or {{{x = 3pi/4}}}