https://file.aiquickdraw.com/mathbot/file/1728021228452yrtr45ok.jpg

Let's go through the steps for the given problem involving a \( 30^\circ \) angle:

### Part a: Drawing the Angle in Standard Position
In standard position, the vertex of the angle is at the origin of the coordinate plane, and the initial side lies along the positive x-axis. The terminal side of the angle is drawn counterclockwise from the x-axis for positive angles.

For \( 30^\circ \), the terminal side would be slightly above the x-axis, in the first quadrant, because the angle is less than \( 90^\circ \). 

### Part b: Converting to Radian Measure
To convert degrees to radians, use the formula:
\[
\text{Radians} = \frac{\pi}{180^\circ} \times \text{Degrees}
\]

For \( 30^\circ \):
\[
\text{Radians} = \frac{\pi}{180^\circ} \times 30^\circ = \frac{\pi}{6}
\]
Thus, \( 30^\circ = \frac{\pi}{6} \) radians.

### Part c: Reference Angle in Degrees and Radians
The reference angle is the smallest angle that the terminal side makes with the x-axis. For angles in the first quadrant (which \( 30^\circ \) is), the reference angle is simply the angle itself.

- **In degrees:** The reference angle is \( 30^\circ \).
- **In radians:** The reference angle is \( \frac{\pi}{6} \).

### Summary:
- **a.** The angle is drawn with its vertex at the origin, initial side along the positive x-axis, and terminal side 30 degrees above the x-axis in the first quadrant.
- **b.** \( 30^\circ = \frac{\pi}{6} \) radians.
- **c.** The reference angle is \( 30^\circ \) or \( \frac{\pi}{6} \) radians.

Would you like me to go into more details about any of these steps?

Here are five questions that build upon this concept:
1. How would you find the reference angle for an angle in the second quadrant?
2. What is the reference angle of \( 120^\circ \) in radians?
3. How would you convert \( 45^\circ \) to radians?
4. What is the radian measure of \( 90^\circ \)?
5. How do you identify the quadrant of an angle based on its radian measure?

**Tip:** To easily convert degrees to radians, remember that \( 180^\circ = \pi \) radians!

For each of the following angles: a) draw the angle in standard position, b) convert to radian measure using exact values, c) name the reference angle in both degrees and radians. The angle given is 30 degrees.

Learn how to draw the 30-degree angle in standard position, convert it to radian measure (π/6), and identify its reference angle in both degrees and radians. This tutorial covers key trigonometric concepts and conversion formulas, suitable for high school students.

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