-4sin^2(t)-3cos(t)=-3

Question

-4sin^2(t)-cos(t)=-3

find all solutions to equation in the interval [0,2pi)

Answer 1

Graph it first.

0 and 2 pi are obvious solutions.

Then substitute 1-cos²t for sin²t and you will convert the equation to a quadratic in is cos x.

Solve the quadratic for the 2 required roots...BUT beware extraneous roots!

MORE DETAIL:

-4(1 - cos²t - 3cos t = -3

4 cos²t - 3cos t -1= 0

Now you have a quadratic equation in cos t which gives

(4 cos t +1)(cos t - 1) = 0 so cos t = 1 and cos t = -1/4

That should get it for you.