Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
1. Measuring Angles
Angles in Standard Position
2:56 minutes
Problem 41a
Textbook Question
Textbook QuestionIn Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Standard Position of an Angle
An angle is said to be in standard position when its vertex is at the origin of a coordinate system and its initial side lies along the positive x-axis. The angle is measured counterclockwise from the initial side. This concept is crucial for determining the location of angles in the coordinate plane and helps in identifying the quadrant in which the terminal side of the angle lies.
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Drawing Angles in Standard Position
Quadrants of the Coordinate Plane
The coordinate plane is divided into four quadrants, each defined by the signs of the x and y coordinates. Quadrant I has positive x and y values, Quadrant II has negative x and positive y, Quadrant III has negative x and y, and Quadrant IV has positive x and negative y. Understanding these quadrants is essential for determining where an angle's terminal side will fall based on its measure.
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Quadratic Formula
Radians and Angle Measurement
Radians are a unit of angular measure where one radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. Angles can be expressed in radians or degrees, but in this context, the problem specifies working with radians. Knowing how to interpret and visualize angles in radians is vital for accurately drawing angles and determining their positions in the coordinate system.
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