Use inverse trigonometric functions to find the solutions of the equation that are in the given interval, and approximate the solutions to four decimal places.

Question

Use inverse trigonometric functions to find the solutions of the equation that are in the given interval, and approximate the solutions to four decimal places.

3 sin² t + 9 sin t + 4 = 0; [-pi/2, pi/2]

t = 

Answer 1

You could let x = sin(t) then 3x² +9x + 4 = 0

Solving by graphing or algebraically,

then x = -0.54257 between

So Sin^-1 (t) = -0.54257 between [-pi/2, pi/2], then t = -0.5735 radians = -32.8588º