Question

How do you find all solutions of the given equation `4sin(theta)-1=0`?

Answer 1

Solve 4sin x - 1 = 0

Ans: `14^@48 and 165^@52`

Explanation:

4sin x = 1
`sin x = 1/4 = 0.25`
By calculator -->
sin x = 0.25 --> `x = 14^@48`
On the trig unit circle, there is another arc x that has the same sin value --> `x = 180 - (14.48) = 165^@52`
General solution:
`x = 14^@48 + k360^@`
`x = 165^@52 + k360^@`