Fundamental Trigonometric Identities

Definitions, Right Triangles, Unit Circle, and Graphs of Trigonometric Functions

Types of Problems:

  • define the trigonometric ratios and functions
  • connect identities to the graphs of the related trigonometric functions
  • connect identities to the unit circle
  • connect identities to the right triangles

Notes & Handouts

Practice 

Video and other resources

SUPERHEXAGON "trick" for remembering trigonometric identities

Digital Resources

DESMOS File: Sine Function
DESMOS File: Cosine Function
DESMOS File: Tangent Function
DESMOS File: Cosecant Function
DESMOS File: Secant Function
DESMOS File: Cotangent Function
DESMOS File: Unit Circle
DESMOS File: Unit Circle and Graphs of Sine and Cosine
These will require a computer
DESMOS Class Activity: Unit Circle class code
DESMOS Class Activity: Unit Circle preview
these require specific software

Reciprocal Identities

Types of Problems:

  • Be able to connect a trigonometric function to its reciprocal trigonometric function​

Notes & Handouts

Practice

​Video and other resources

DESMOS File: Reciprocal Identities

Quotient Identities

​Types of Problems:

  • Be able to connect tangent function to its quotient of trigonometric functions
  • Be able to connect cotangent function to its quotient of trigonometric functions

​Notes & Handouts

​Practice

​Video and other resources

Pythagorean Identities

​Types of Problems:

  • Connect unit circle to Initial Pythagorean Identity
  • Be able to derive the Nine Pythagorean Obvious Identities from the initial identity and algebraic manipulations
  • Be able to use difference of two squares factoring to determine eight additional Pythagorean Identities

​Practice

​Video and other resources

​Notes & Handouts

Cofunction Identities​

​​​Types of Problems:

  • Be able to connect the related ratios between a function and its co-function
  • Be able to connect the graph of the function and the impact of the transformations on the graph of the co-function

​​​Notes & Handouts

​Practice

​Video and other resources

Even/Odd Identities

​​Types of Problems:

  • Be able to connect the impact of a negative sign on the trigonometric functions
  • Be able to classify a function as even or odd  

​​Notes & Handouts

Practice

​Video and other resources

DESMOS File: Even Odd Identities