To find the referred angle for -170°, we first need to understand what a referred angle (or reference angle) is. The reference angle is the positive acute angle that the terminal side of the given angle makes with the x-axis.
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Sketching the angle -170°:
- Since -170° is a negative angle, we measure it in the clockwise direction from the positive x-axis.
- Starting from the positive x-axis and moving clockwise, -170° lands in the fourth quadrant.
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Finding the corresponding positive angle:
- To convert the negative angle to a positive angle, we can add 360°: \[ -170° + 360° = 190° \]
- This indicates that the terminal side of -170° is the same as that of 190°.
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Finding the referred angle:
- The referred angle is the positive acute angle that forms with the x-axis. Since 190° is in the third quadrant, we can find the referred angle by subtracting it from 180°: \[ Referred:angle = 190° - 180° = 10° \]
In conclusion, the referred angle for -170° is 10°.