Questions and Answers
What is the reference angle for 135°?
45°
What is the reference angle for 450°?
90°
What is the reference angle for -2π/3?
π/3
What is the reference angle for 11π/4?
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In which quadrant does the angle 135° lie?
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What is the equivalent angle of 450° when adjusted within a full rotation?
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What is the reference angle for -2π/3?
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Which of the following angles is equivalent to 11π/4?
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What is the range of reference angles for standard position angles?
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Study Notes
Angle 135°
- Lies in the second quadrant.
- Standard position: Starts from the positive x-axis and rotates counter-clockwise to 135°.
- Reference angle: 180° - 135° = 45°.
Angle 450°
- Equivalent to 90° when reduced to a single rotation (450° - 360°).
- Lies in the first quadrant.
- Standard position: Rotates counter-clockwise to 90°.
- Reference angle: 90° - 90° = 0° (90° itself is the angle).
Angle -2π/3
- Equivalent to +π/3 when added to 2π (positive full rotation).
- Lies in the third quadrant.
- Standard position: Starts from the positive x-axis and rotates clockwise to -2π/3.
- Reference angle: π + 2π/3 = 5π/3; so reference angle = 5π/3 - π = 2π/3.
Angle 11π/4
- Equivalent to 3π/4 when reduced by 2π (11π/4 - 8π/4).
- Lies in the second quadrant.
- Standard position: Rotates counter-clockwise to get to 3π/4.
- Reference angle: 180° - 3π/4 (or π - 3π/4 = π/4).
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Description
This quiz involves sketching angles in standard position and identifying their reference angles. It covers various scenarios, including positive and negative angles as well as radians. Test your understanding of angle representation and reference angles.
