Is it possible to solve sinx=−13√sin⁡x=−13 in exact terms?

Answer 1

Let y = sqrt(sinx)

Then y^2 = sinx

y^2 = -13*y = -13

y^2 + 13y + 13 = 0

y=[-13 +or- sqrt( 169 - 52)] / 2

y=[-13 +or- sqrt(117)]/2

10^2 = 100 < 117 < 121 = 11^2

So 10 < sqrt(117) < 11

-3 < -13 + sqrt(117) < -2

-3/2 < y < -1

-3/2 < sine < -1

The answer is NO!!!

sine function must be between -1 and 1