How many solutions does 
sin2(x) (8cos(x) − 1) = 0
 have in the interval 
[0, 𝜋]
?

We are tasked with solving the equation \( \sin^2(x)(8\cos(x) - 1) = 0 \) in the interval \([0, \pi]\).

### Step-by-Step Solution:

1. The equation can be factored as:
   \[
   \sin^2(x) = 0 \quad \text{or} \quad 8\cos(x) - 1 = 0
   \]

2. Solve for \( \sin^2(x) = 0 \):
   - \( \sin^2(x) = 0 \) implies \( \sin(x) = 0 \).
   - In the interval \([0, \pi]\), \( \sin(x) = 0 \) at \( x = 0 \) and \( x = \pi \).

3. Solve for \( 8\cos(x) - 

How many solutions does sin^2(x)(8cos(x) − 1) = 0 have in the interval [0, 𝜋]?

Explore the solution to the trigonometric equation sin^2(x)(8cos(x) − 1) = 0 within the interval [0, π]. This step-by-step guide covers key trigonometric concepts, such as solving for sin(x) and cos(x) using the Zero Product Property. Suitable for Grades 10-12 students studying trigonometry.

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