Solve each trigonometric equation for the given domain

Question

Sin theta= -1/2 for -700° Less than equal to theta less than equal to 700°

how do u know what to add and subtract by

Answer 1

sin(theta) = -1/2

theta = 210 or 330 or either + n(360) where n = any integer

-700 < theta < 700

theta = -570, -390, -210, -30, 150, 330, 510, or 690

reference angle is 30 degrees below the x axis, 210 or -30, add multiples of 360 to each to get every possible angle

Answer 2

sinθ = -1/2; θ = 210° + 360°n or θ = 330° + 360°n;

-700° ≤ 210° + 360°n ≤ 700°;

-910°≤360°n ≤ 490°; - 2 - 19/36 ≤ n ≤ 1 + 13/36 So, n = - 2, - 1, 0, 1 we have θ = 210°, 570°, - 150°, - 510°

-700° ≤ 330° + 360°n ≤ 700°;; -1030° ≤ 360°n ≤ 370°; - 2 - 31/36 ≤ n ≤ 1 + 1/37; n = -2, - 1, 0, 1

θ = - 390°, - 30°, 330°, 690°