Question

The number of solutions of the equation \[ 3 \sin^2 x - 7 \sin x + 2 = 0 \] in the interval \( [0, 5\pi] \) is

• A. 0
• B. 5
• C. 6
• D. 7

Hint:

For trigonometric equations, first solve the corresponding equation for the trigonometric function and then determine how many solutions lie within the given interval.

Answer 1

The Correct Option is C

The equation is solved by finding the solutions of the corresponding quadratic equation in \( \sin x \) and determining how many solutions lie in the interval \( [0, 5\pi] \).
The number of solutions is 6.