SOLUTION: 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.

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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.
Answer by jim_thompson5910(35256) About Me  (Show Source):
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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: http://www.regentsprep.org/Regents/math/algtrig/ATT5/600px-Unit_circle_angles_svg.jpg)

The two solutions are x+=+pi%2F4 or x+=+3pi%2F4