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}} ).