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Reference Angles & Unit Circle
Section 4.2 Precalculus PreAP/Dual, Revised ©2017 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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§4.2: Reference Angles and Unit Circle
Reference angle is a positive acute angle formed by the terminal side of ө and the 𝒙-axis. They are viewed as linear pairs. (Think: REFER’s back to the 𝒙-axis) The main angle should be within 0 and 360 degrees. No reference trigonometric values of measure are greater than 𝟗𝟎° or less than to 𝟎° Quadrant I: 𝜽 Quadrant II: 𝟏𝟖𝟎°−𝜽 Quadrant III: 𝜽−𝟏𝟖𝟎° Quadrant IV: 𝟑𝟔𝟎°−𝛉 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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Reference Angle Quadrants
11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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§4.2: Reference Angles and Unit Circle
Example 1 Determine the reference angle for 𝜽=𝟏𝟑𝟓° 135° 45° 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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§4.2: Reference Angles and Unit Circle
Example 2 Determine the reference angle for 𝛉=− 𝟏𝟏𝝅 𝟔 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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§4.2: Reference Angles and Unit Circle
Example 3 Determine the reference angle for 𝜽=𝟑 𝑹𝒂𝒅𝒊𝒂𝒏𝒔 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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§4.2: Reference Angles and Unit Circle
Your Turn Determine the reference angle for 𝛉=− 𝝅 𝟕 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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Degrees in the Unit Circle – 45°, 45°, 90°
II III IV 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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§4.2: Reference Angles and Unit Circle
Conversions Convert 𝟒𝟓° to Radian Mode 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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Radians in the Unit Circle – 45°, 45°, 90°
II III IV 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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§4.2: Reference Angles and Unit Circle
Right Triangles – 45°, 45°, 90° triangles (Drawing not to scale) Radius = 1 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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§4.2: Reference Angles and Unit Circle
Reminder 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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Creating the Unit Circle – 45°, 45°, 90°
11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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Degrees in the Unit Circle – 30°, 60°, 90°
II III IV 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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§4.2: Reference Angles and Unit Circle
Conversions Convert 𝟑𝟎° to Radian Mode 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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Radians in the Unit Circle – 30°, 60°, 90°
II III IV 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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Creating the Unit Circle – 30°, 60°, 90°
11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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Degrees in the Unit Circle – 30°, 60°, 90°
II III IV 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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§4.2: Reference Angles and Unit Circle
Conversions Convert 𝟔𝟎° to Radian Mode 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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Creating the Unit Circle – 30°, 60°, 90°
11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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Degrees in the Unit Circle – 30°, 60°, 90°
II III IV 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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§4.2: Reference Angles and Unit Circle
Assignment Complete the Unit Circle and Worksheet 1 11/10/ :27 AM §4.2: Reference Angles and Unit Circle

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