Question

How do you find all values of t in the interval `[0,2pi]` satisfying the given equation `4cos^2t+4=5`?

Answer 1

`pi/3, (2pi)/3, (4pi)/3, (5pi)/3`

Explanation:

Solve for `cos t` as follows;

`4 cos^2 t= 5-4=1`

`cos^2 t =1/4`

`cos t= +1/2, -1/2`

For `cos t= +1/2`, `t` would lie in Ist and IVth Quadrant. It would be `pi/3` or `-pi/3= 2pi-pi/3= (5pi)/3` in the interval `[0,2pi]`.

For `cos t= -1/2, t` would lie in IInd and IIIrd Quadrant. It would be `pi-pi/3= (2pi)/3, or pi+pi/3= (4pi)/3`