Find the approximate value in both radians and degrees using a calculator

Question

csc^-1 (-6.5757) round to four decimal places as needed

Answer 1

csc^-1 -6.5757

sin^-1 0.152075

8.7472

Answer 2

Hi Aireeyon G.,

Since csc^-1(-6.5757) = θ, therefore csc(θ) = -6.5757.

And csc(θ) = Hypotenuse/Side Opposite (H/SO).

Therefore csc(θ) = H/SO = -6.5757/1, where 6.5757 is the hypotenuse and -1 is the side opposite. This puts this triangle in either quadrant 3 or 4 of Cartesian coordinates, since side opposite are y-values (and in this case a negative y-value), and the hypotenuse is always the positive square root of the Pythagorean theorem.

And sin(θ) = SO/H, therefore sin(θ) = -1/6.5757.

Therefore θ = sin^-1(-1/6.5757) = -0.1527 radians, or -8.7472°, rounded to four decimal places. Set your calculator to degrees to get degrees, and set to radians to get radians.

I hope this helps, Joe.