SOLUTION: Find all solutions of the equation in the interval [0,2π). csc(theta) - sqrt2 = 0 Write your answer in radians in terms of π. If there is more than one solution, s

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions of the equation in the interval [0,2π). csc(theta) - sqrt2 = 0 Write your answer in radians in terms of π. If there is more than one solution, s      Log On


   

Question 1036318: Find all solutions of the equation in the interval [0,2π).
csc(theta) - sqrt2 = 0
Write your answer in radians in terms of π.
If there is more than one solution, separate them with commas.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
csc%28theta%29+-+sqrt%282%29+=+0
csc%28theta%29+=+sqrt%282%29
1%2F%28sin%28theta%29%29+=+sqrt%282%29
sin%28theta%29+=+1%2F%28sqrt%282%29%29
sin%28theta%29+=+sqrt%282%29%2F2

Use the unit circle

Image Source: https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png

to find points on the unit circle that have y coordinates of sqrt%282%29%2F2

The corresponding values of theta are theta+=+pi%2F4 and theta+=+3pi%2F4


So the two solutions, in the interval [0,2π) are pi%2F4 and 3pi%2F4