Let's solve the equation \( 4 \sin x - 2 = 0 \).

### Step 1: Isolate \( \sin x \)
\[
4 \sin x - 2 = 0
\]
Add 2 to both sides:
\[
4 \sin x = 2
\]
Divide both sides by 4:
\[
\sin x = \frac{2}{4} = \frac{1}{2}
\]

### Step 2: Solve for \( x \)
Now we need to find the values of \( x \) such that \( \sin x = \frac{1}{2} \).

The general solutions for \( \sin x = \frac{1}{2} \) are given by:
\[
x = \frac{\pi}{6} + 2n\pi \quad \text{or} \quad x = \pi - \frac{\pi}{6} + 2n\pi
\]
Simplifying:
\[
x = \frac{\pi}{6} + 2n\pi \quad \text{or} \quad x = \frac{5\pi}{6} + 2n\pi
\]
where \( n \) is any integer.

### Final Answer:
The solutions are:
\[
x = \frac{\pi}{6} + 2n\pi \quad \text{or} \quad x = \frac{5\pi}{6} + 2n\pi
\]
where \( n \) is an integer.

Would you like more details or have any questions?

---

Here are five related questions to deepen your understanding:
1. What is the general solution for \( \sin x = -\frac{1}{2} \)?
2. How would you solve \( 3 \sin x + 1 = 0 \)?
3. What are the solutions for \( \cos x = \frac{1}{2} \)?
4. How does the unit circle help in solving trigonometric equations?
5. What are the steps to solve \( 5 \sin x - 3 = 0 \)?

**Tip:** Remember that sine and cosine functions are periodic with a period of \( 2\pi \), which is why we add \( 2n\pi \) to the solutions.

Learn how to solve the trigonometric equation 4sin(x) - 2 = 0 with step-by-step explanations. This problem focuses on solving for sin(x) = 1/2 and uses the general solution for trigonometric equations. Ideal for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation