Questions and Answers
What is the amplitude for sin/cos?
What is the amplitude for tan?
None
What is the period for sin/cos?
360 divided by the absolute value of the number after sin/cos
What is the period for tan?
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What are phase shifts?
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What are vertical shifts?
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What is the midline?
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Describe cosine graphs.
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Describe sine graphs.
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What is a reference angle?
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Define Q1.
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Define Q2.
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Define Q3.
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Define Q4.
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How do you find coterminal angles?
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How do you convert angles to radians?
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How do you convert radians to angles?
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Fill in the blank: $cos^2 + sin^2 = ______$
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Fill in the blank: $cot^2 + 1 = ______$
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Fill in the blank: $tan^2x + 1 = ______$
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What is Csc?
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What is Sec?
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What is Cot?
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What is Tan?
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What is Cot?
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What is Sin?
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What is Cos?
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What is Tan?
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What is Csc?
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What is Sec?
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What is Cot?
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Study Notes
Trigonometric Functions and Their Properties
- Amplitude for sin/cos: Defined as the absolute value of the coefficient before the sine or cosine function.
- Amplitude for tan: Tan does not have an amplitude.
- Period for sin/cos: Calculated as 360 degrees divided by the absolute value of the coefficient after sine or cosine.
- Period for tan: Found by dividing 180 degrees by the absolute value of the coefficient after tan.
- Phase shifts: The movement of the graph left or right, where addition indicates a left shift and subtraction indicates a right shift.
- Vertical shifts: Movement of the graph up or down outside of parentheses, where addition indicates an upward shift and subtraction indicates a downward shift.
- Midline: The baseline for the sine and cosine functions, typically at 0 unless a vertical shift is applied.
Graph Characteristics
- Cosine graphs: Characterized by their single curve and beginning above the origin.
- Sine graphs: Exhibit two curves forming an "S" shape, starting at the origin (0).
Angle Concepts
- Reference angle: The acute angle formed between the terminal side of the angle and the x-axis.
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Quadrants:
- Q1: Represents the angle itself.
- Q2: Calculated as 180 degrees minus the angle.
- Q3: Derived by subtracting 180 degrees from the angle value.
- Q4: Calculated as 360 degrees minus the angle.
Coterminal Angles and Angle Conversion
- Finding coterminal angles: Generate coterminal angles by adding or subtracting 360 degrees.
- Converting angles to radians: Multiply the angle in degrees by π/180.
- Converting radians to angles: Multiply the angle in radians by 180/π.
Fundamental Identities
- Pythagorean Identity: ( \cos^2 x + \sin^2 x = 1 ).
- Csc and cot identities: ( \cot^2 x + 1 = \csc^2 x ).
- Secant identity: ( \tan^2 x + 1 = \sec^2 x ).
Trigonometric Ratios
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Reciprocal relationships:
- Cosecant (csc): ( \csc x = \frac{1}{\sin x} ).
- Secant (sec): ( \sec x = \frac{1}{\cos x} ).
- Cotangent (cot): ( \cot x = \frac{1}{\tan x} ).
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Basic ratio definitions:
- Tangent (tan): ( \tan x = \frac{\sin x}{\cos x} ).
- Cotangent (cot): ( \cot x = \frac{\cos x}{\sin x} ).
- Sine (sin): ( \sin x = \frac{\text{opposite}}{\text{hypotenuse}} ).
- Cosine (cos): ( \cos x = \frac{\text{adjacent}}{\text{hypotenuse}} ).
- Tangent (tan): ( \tan x = \frac{\text{opposite}}{\text{adjacent}} ).
- Cosecant (csc): ( \csc x = \frac{\text{hypotenuse}}{\text{opposite}} ).
- Secant (sec): ( \sec x = \frac{\text{hypotenuse}}{\text{adjacent}} ).
- Cotangent (cot): ( \cot x = \frac{\text{adjacent}}{\text{opposite}} ).
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Description
This quiz focuses on key concepts in Algebra 2 Trigonometry, providing definitions for terms such as amplitude, period, and phase shifts. Ideal for review or study, these flashcards will help solidify your understanding of trigonometric functions and their properties. Perfect for students preparing for exams or needing a quick refresher.
