Question

Can someone help me solve csc^2 x = 5 algebraically over the interval 0 <= x < 2pi?

Answer 1

So far, I have sin x = 1/sqrt5

Answer 2

when we take square root we get 2 solutions \[\sqrt{x^2}= \pm x \]

Answer 3

Yes

Answer 4

and since we cant leave the radical sign at the denominator we should multiply top and bottom of the fraction by the denominator

Answer 5

So 1/sqrt5 is basically sqrt5/5

Answer 6

x = sin^-1 sqrt5/5

Answer 7

yes right now i think we should use calculator
to find exact values
but here is sign chat that helps us to figure out the quadrant