Question

How do you find all solutions of the equation `sin(3x-15)=1/2`?

Answer 1

There is another way. Trig table gives:
`sin (3x - 15 deg) = 1/2 = sin 30 deg`. Trig unit circle gives 2 answers:

a. `3x - 15 = 30 -> 3x = 45 -> x = 15 deg`

b. `3x - 15 = (180) - 30 -> 3x = 150 + 15 = 165 -> x = 55 deg`

Check:
`x = 15 -> 3x -15 = 30 -> sin 30 = 1/2. OK`
`x = 55 -> 3x - 15 = 165 - 15 = 150 -> sin 150 = 1/2. OK`