Solve the equation for θ if 0° ≤ θ < 360°. (Enter your answers as a comma-separated list.) 4 sin θ − 2 csc θ = 0

Answer 1

Hi, Madison:

The way to do these types of problem is to convert all trig ratios to sin and cos, then solve the resulting equation. Let's do it.

4 sinθ - 2 cosecθ = 0

4sinθ - 2/sinθ = 0

4sin²θ - 2 = 0 . . . . . . . we can diviide through by sinθ, provided it isn't zero

4sin²θ = 2

sin²θ = 1/2

sinθ = 1/√2

θ = 45⁰ or 180⁰ - 45⁰ = 135⁰

Solution set: {45⁰, 135⁰}

Note: sinθ can't be zero in the 3rd line, above, because then cosec would be undefined (can't divide by zero!)