Find all solutions, to the nearest tenth of a degree, in the interval 0° ≤ 𝜃 < 360°.

Question

7 sin² 𝜃 - 2 sin 𝜃 = 5

Answer 1

let x= sin(theta)

7x^2 -2x =5

7x^2 -2x -5 = 0

factor

(7x+5)(x-1) = 0

set each factor equal to zero

x = 1, -5/7

sin(theta) = 1, -5/7

theta = sin^-1(1), sin^-1(-5/7)

theta = 90 degrees

or 180+45.6 = 225.6 degrees

or 360-45.6 = 314.4 degrees