\#1.) Graph the angles below on the Unit Circle. Label the axes. Draw the initial and terminal side - Draw an arrow representing the span of the angle Label the reference angle in degrees

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1. **Draw the Unit Circle and Axes**

- Draw a circle with center at the origin, $$ (0,0) $$, and radius 1.
   - Draw two perpendicular lines through the origin to represent the $$x$$–axis and $$y$$–axis.
   - Label the positive $$x$$–axis, negative $$x$$–axis, positive $$y$$–axis, and negative $$y$$–axis.

2. **Draw the Initial Side**

- The initial side of any angle in standard position always lies along the positive $$x$$–axis.
   - Mark the ray beginning at $$ (0,0) $$ and extending to $$ (1,0) $$.

3. **Plotting the Angle**

- Choose an angle to graph. For example, consider an angle of $$150^\circ$$.
   - An angle in standard position has its vertex at the origin, with its initial side along the positive $$x$$–axis.
   - Measure $$150^\circ$$ counterclockwise from the initial side.
   - Draw an arrow along the circular arc from $$0^\circ$$ to $$150^\circ$$ to show the span of the angle.

4. **Draw the Terminal Side**

- From the origin, draw a ray in the direction of $$150^\circ$$.
   - Since $$150^\circ$$ is in the second quadrant, the terminal side will lie between the positive $$y$$–axis and the negative $$x$$–axis.
   - Extend this ray until it intersects the unit circle.

5. **Label the Reference Angle**

- The reference angle is the acute angle between the terminal side and the horizontal $$x$$–axis.
   - For angles in the second quadrant, the reference angle is given by:
     $$
     \text{Reference Angle} = 180^\circ - \theta
     $$
     Thus for $$\theta = 150^\circ$$:
     $$
     \text{Reference Angle} = 180^\circ - 150^\circ = 30^\circ
     $$
   - Label this $$30^\circ$$ in the region between the terminal side and the negative $$x$$–axis.

6. **Final Diagram Sketch Description**

- **Circle:** A circle with center $$ (0,0) $$ and radius 1.
   - **Axes Labels:** Horizontal line labeled as the $$x$$–axis and vertical line labeled as the $$y$$–axis.
   - **Initial Side:** A ray along the positive $$x$$–axis starting at the origin.
   - **Angle Span:** An arc starting at the positive $$x$$–axis and sweeping counterclockwise to $$150^\circ$$, with an arrow showing the direction.
   - **Terminal Side:** A ray from the origin making an angle of $$150^\circ$$ with the positive $$x$$–axis, intersecting the circle in the second quadrant.
   - **Reference Angle:** A small angle of $$30^\circ$$ between the terminal side and the horizontal line (extended from the negative $$x$$–axis or by dropping a perpendicular to the $$x$$–axis).

This step-by-step method allows you to graph any given angle on the unit circle by following the same procedure.
To graph an angle on the unit circle: 1. **Draw the Unit Circle and Axes**: Sketch a circle with center at (0,0) and axes labeled. 2. **Draw the Initial Side**: Start from the positive x-axis. 3. **Plot the Angle**: Measure the angle counterclockwise from the initial side. 4. **Draw the Terminal Side**: Extend the ray to the circle. 5. **Label the Reference Angle**: Find the acute angle between the terminal side and the x-axis. Example for $$150^\circ$$: - Draw the circle and axes. - Start at the positive x-axis. - Measure $$150^\circ$$ counterclockwise. - Draw the terminal side intersecting the circle. - Label the reference angle as $$30^\circ$$. This method helps visualize any angle on the unit circle by following these steps.

\#1.) Graph the angles below on the Unit Circle. Label the axes. Draw the initial and terminal side - Draw an arrow representing the span of the angle Label the reference angle in degrees

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