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, $\frac{\pi}{2} = 90^\circ$.