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Questions and Answers
What does the sine function represent in relation to the unit circle?
What does the sine function represent in relation to the unit circle?
What is the period of a sine function?
What is the period of a sine function?
In which scenario is the tangent function undefined?
In which scenario is the tangent function undefined?
What does the amplitude of a function describe?
What does the amplitude of a function describe?
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What defines the range of a trigonometric function?
What defines the range of a trigonometric function?
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Which statement about the standard position of an angle is true?
Which statement about the standard position of an angle is true?
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What does the cotangent function measure?
What does the cotangent function measure?
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What is the significance of the initial side of an angle in a circle?
What is the significance of the initial side of an angle in a circle?
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Study Notes
Pre-Calculus Definitions
- Radian: The measure of a central angle whose arc length equals the radius of the circle.
- Angle: Formed by two rays sharing a common endpoint (vertex). Measured in degrees (°).
- Vertex: The common endpoint of the rays forming an angle.
- Sides: The rays that form an angle.
- Initial Side: The ray where the angle begins.
- Terminal Side: The ray where the angle ends.
- Standard Position: An angle is in standard position if its vertex is at the origin and its initial side lies on the positive x-axis.
- Coterminal Angles: Angles in standard position with the same terminal side.
- Linear Measure: The length of the arc that subtends an angle.
- Reference Angle: The smallest positive angle between the terminal side and the x-axis.
- Unit Circle: A circle with a radius of 1, centered at the origin, used to define trigonometric functions. Its equation is x² + y² = 1.
Trigonometric Functions (Week 2)
- Sine function: sin θ = y
- Cosine function: cos θ = x
- Tangent function: tan θ = y/x (x ≠ 0)
- Cotangent function: cot θ = x/y (y ≠ 0)
- Cosecant function: csc θ = 1/y (y ≠ 0)
- Secant function: sec θ = 1/x (x ≠ 0)
Definitions (Weeks 3 & 4)
- Domain: All possible x-values (inputs) of a function.
- Range: All possible y-values (outputs) of a function.
- Amplitude: Half the distance between the maximum and minimum values of a trigonometric function.
- Period: The horizontal length of one complete cycle of a trigonometric function.
- Phase Shift: The horizontal displacement of a trigonometric function from its usual position.
Identities (Week 5)
- Identity: An equation that is true for all values in the domain of the variables involved. Trigonometric identities involve trigonometric expressions.
Inverse Functions (Week 6)
- Inverse Function: Reverses the action of a function, denoted by f⁻¹.
- Interval: A set of real numbers between two given numbers.
- Fundamental Solution Set (FSS): The set of all values that satisfy a given equation.
Equations (Week 6 )
- Trigonometric Equation: An equation that involves trigonometric expressions.
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Description
Test your understanding of key pre-calculus definitions and concepts related to angles, radian measures, and the unit circle. This quiz covers essential terms essential for mastering trigonometric functions and their applications. Prepare to enhance your mathematical vocabulary and comprehension!
