$ ext{How to Find the Reference Angle Not on Unit Circle}$
Answer 1
Thomas Walker
To find the reference angle of an angle not on the unit circle, follow these steps:
1. Determine the quadrant in which the angle is located.
2. Use the following rules based on the quadrant to find the reference angle:
For an angle $\theta$ in the first quadrant, the reference angle is $\theta$.
For an angle $\theta$ in the second quadrant, the reference angle is $180^\circ – \theta$.
For an angle $\theta$ in the third quadrant, the reference angle is $\theta – 180^\circ$.
For an angle $\theta$ in the fourth quadrant, the reference angle is $360^\circ – \theta$.
Example: Find the reference angle for $210^\circ$.
Since $210^\circ$ is in the third quadrant, we use the rule for the third quadrant:
$\text{Reference Angle} = 210^\circ – 180^\circ = 30^\circ$
Therefore, the reference angle for $210^\circ$ is $30^\circ$.
Answer 2
Alex Thompson
To find the reference angle of an angle not on the unit circle, follow these steps:
1. Identify the quadrant of the angle.
2. Use the appropriate formula based on the quadrant:
In the first quadrant: $ heta$
In the second quadrant: $180^circ – heta$
In the third quadrant: $ heta – 180^circ$
In the fourth quadrant: $360^circ – heta$
Example: Find the reference angle for $300^circ$.
$300^circ$ is in the fourth quadrant, so:
$ ext{Reference Angle} = 360^circ – 300^circ = 60^circ$
The reference angle for $300^circ$ is $60^circ$.
Answer 3
William King
To find the reference angle:
1. Determine the quadrant.
2. Use the quadrant-specific rule:
1st quadrant: $ heta$
2nd quadrant: $180^circ – heta$
3rd quadrant: $ heta – 180^circ$
4th quadrant: $360^circ – heta$
Example: For $135^circ$ in the second quadrant:
$ ext{Reference Angle} = 180^circ – 135^circ = 45^circ$
Thus, the reference angle is $45^circ$.
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