Question

Find all solutions if 0° ≤ θ < 360°. Verify your answer graphically. (Enter your answers as a comma-separated list.)? `sin 2θ = −1/2`

Answer 1

See below

Explanation:

Let’s say `2theta` is equal to `u`:
`sinu= -1/2`
`u= 210^@+-360^@n`
`u= 330^@+-360^@n`

Now let’s solve for theta:
`theta= 105^@ +-180^@n`
`theta= 165^@ +-180^@n`

Now find all feasible solutions by adding or subtracting `180^@` to all the solutions:
`theta= 105^@, 165^@, 285^@, 345^@`