Question

Solve the following trigonometric equation for 0 ≤ theta < 2pi

sin (theta) sec (theta) - 2 sin (theta) = 0
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Answer 1

The solutions for theta in the interval 0 to 2pi are 0, pi/3, pi, and 5pi/3.

Step-by-step explanation:

To solve the trigonometric equation sin(theta) sec(theta) - 2 sin(theta) = 0 for 0 ≤ theta < 2pi, we start by factoring the equation: sin(theta)(sec(theta) - 2) = 0

This equation suggests two possible solutions: either sin(theta) = 0 or sec(theta) - 2 = 0.

Solving these separately:

sin(theta) = 0: This occurs when theta = 0, pi, or 2pi.

sec(theta) - 2 = 0: Which simplifies to cos(theta) = 1/2.

This occurs at theta = pi/3 or 5pi/3.

Summarizing, the solutions for theta within the given interval are: 0, pi/3, pi, 5pi/3