Algebra 2 Trigonometry Review Flashcards

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.
• 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

• 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} ).
• 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}} ).

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.