$ ext{How to find reference angle not on unit circle}$
Answer 1
Daniel Carter
Given an angle of 210 degrees, find the reference angle.
Step 1: Determine the quadrant in which the angle lies. 210 degrees is in the third quadrant.
Step 2: Use the formula for finding the reference angle in the third quadrant: $\theta_{ref} = \theta – 180^\circ$.
Step 3: Substitute the given angle into the formula: $\theta_{ref} = 210^\circ – 180^\circ$.
Step 4: Simplify: $\theta_{ref} = 30^\circ$.
Answer 2
Emma Johnson
Given an angle of 135 degrees, find the reference angle.
Step 1: Determine the quadrant in which the angle lies. 135 degrees is in the second quadrant.
Step 2: Use the formula for finding the reference angle in the second quadrant: $ heta_{ref} = 180^circ – heta$.
Step 3: Substitute the given angle into the formula: $ heta_{ref} = 180^circ – 135^circ$.
Step 4: Simplify: $ heta_{ref} = 45^circ$.
Answer 3
Maria Rodriguez
Given an angle of 300 degrees, find the reference angle.
Step 1: Determine the quadrant in which the angle lies. 300 degrees is in the fourth quadrant.
Step 2: Use the formula for finding the reference angle in the fourth quadrant: $ heta_{ref} = 360^circ – heta$.
Step 3: Substitute the given angle into the formula: $ heta_{ref} = 360^circ – 300^circ$.
Step 4: Simplify: $ heta_{ref} = 60^circ$.
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