Find all values of x in the interval [0°, 360°) that satisfy the equation. Round approximate answers to the nearest tenth of a
degree.
-sin 2x = csc 2x
A) {45°, 135°}
B) {45°, 135°, 225°, 315°}
C) {0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°}
D) {45°, 225°}

Question

Quizplus · Accepted Answer

The equation sin 2x = csc 2x can be rewritten as sin 2x = 1/sin 2x, which simplifies to sin^2 2x = 1. This equation is satisfied when sin 2x = ±1. Solving for 2x gives 2x = 90°, 270° (for sin 2x = 1) and 2x = 90°, 270° (for sin 2x = -1) within one cycle (0° to 360°). Dividing by 2 to solve for x gives x = 45°, 135°, 225°, 315°.

Find All Values of X in the Interval [0°, 360°)