solve for theta      tantheta over 2 = 6 over 2.5

The given equation is:

\[
\tan\left(\frac{\theta}{2}\right) = \frac{6}{2.5}
\]

### Step 1: Simplify the right-hand side

\[
\tan\left(\frac{\theta}{2}\right) = \frac{6}{2.5} = 2.4
\]

### Step 2: Take the arctangent (inverse tangent) of both sides to solve for \(\frac{\theta}{2}\):

\[
\frac{\theta}{2} = \tan^{-1}(2.4)
\]

### Step 3: Calculate the arctangent value:

\[
\frac{\theta}{2} \approx 1.17 \text{ radians} \text{ or } 67.38^\circ
\]

### Step 4: Multiply by 2 to get \(\theta\):

\[
\theta \approx 2 \times 1.17 = 2.34 \text{ radians} \text{ or } 134.76^\circ
\]

### Final Answer:

\[
\theta \approx 2.34 \text{ radians} \text{ or } 134.76^\circ
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How does the unit (radians vs degrees) affect trigonometric functions?
2. What is the general solution for \(\tan(x) = k\) in trigonometry?
3. How do you convert between radians and degrees?
4. How does the value of \(\theta\) change with different ratios for \(\tan(\frac{\theta}{2})\)?
5. Can \(\theta\) have multiple solutions depending on the context?

**Tip:** Always remember that the output of the inverse tangent function is usually restricted to \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\) radians (or \(-90^\circ\) to \(90^\circ\)).

Learn how to solve the trigonometric equation tan(theta/2) = 6/2.5 step-by-step. This problem involves trigonometry and the use of the inverse tangent function. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation