The expression \(0 < \theta < \frac{\pi}{2}\) means that the angle \(\theta\) lies between 0 and \(\frac{\pi}{2}\) radians (or 0 and 90°) on the unit circle. In this range:

1. The angle \(\theta\) is measured in radians.
2. \(0 < \theta\) implies that \(\theta\) is positive, starting just after 0 radians.
3. \(\theta < \frac{\pi}{2}\) means that \(\theta\) is less than \(\frac{\pi}{2}\), which is equivalent to 90°.
4. This range is the **first quadrant** of the unit circle.

In this interval:
- The sine of \(\theta\) is positive.
- The cosine of \(\theta\) is also positive.
- The tangent of \(\theta\) is positive.

Would you like further details or have any questions?

Here are some related questions:

1. What is the sine, cosine, and tangent in the range \(0 < \theta < \frac{\pi}{2}\)?
2. How is \(\theta\) measured in radians versus degrees?
3. What are the characteristics of angles in the first quadrant?
4. How does the unit circle help in understanding trigonometric functions?
5. Why do sine, cosine, and tangent remain positive in this range?

**Tip:** To convert radians to degrees, remember that \(\pi\) radians equals 180°. So, \(\frac{\pi}{2} = 90^\circ\).

Explore the meaning of 0 < θ < π/2, a key concept in trigonometry, where the angle θ is between 0 and 90 degrees in radians. Learn about sine, cosine, and tangent in this first quadrant range, where all trigonometric functions are positive. Suitable for Grades 10-12 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