Sketch the angle then find its reference angle -170^•

Question

GPT-4o mini · Answer

To find the reference angle for $-170^\circ$, we follow these steps: 1. **Locate the Angle**: Since $-170^\circ$ is a negative angle, it is measured clockwise from the positive x-axis. 2. **Find the Positive Equivalent**: To convert the negative angle to a positive angle, add $360^\circ$: $$ -170^\circ + 360^\circ = 190^\circ $$ This means that $-170^\circ$ is coterminal with $190^\circ$. 3. **Determine the Quadrant**: The angle $190^\circ$ lies in the third quadrant since $180^\circ < 190^\circ < 270^\circ$. 4. **Calculate the Reference Angle**: The reference angle is the acute angle formed with the x-axis. In the third quadrant, the reference angle can be found by subtracting $180^\circ$ from the angle: $$ 190^\circ - 180^\circ = 10^\circ $$ The reference angle for $-170^\circ$ is therefore $10^\circ$. ### Sketch of the Angle: 1. Draw a standard coordinate system with axes labeled. 2. From the positive x-axis, move clockwise to $-170^\circ$. 3. This position corresponds to an angle of $190^\circ$ in the standard counterclockwise direction, situating the terminal side in the third quadrant. 4. Mark the reference angle at $10^\circ$ from the negative x-axis back to the terminal side. ### Final Answer: The reference angle for $-170^\circ$ is $10^\circ$.