Unit Circle & Graphing

Essential Question: How can we model periodic (repeating) and fluctuating (oscillating) data?


1) Degree and Radian Measurements and Conversion

2) Coterminal and Reference Angles

Trig Operations

3) Trig on a Coordinate Plane

4) Completing the Unit Circle:

5) Exact Trig Ratios on a Unit Circle:

6) Inverse Trig Ratios on a Unit Circle:

7) Order of Operations with Trig Ratios:

Graphing Trig Functions

8) Graphing Sin and Cosine from the Unit Circle:

9) Transformations of sin and cos: Amplitude and Period

10) Transformation of sin and cos: Vertical Shift (shift the x-axis or "midline")

11) Transformation of sin and cos: Horizontal Shift (shift the y-axis or Phase Shift)

12) Identify Parts of a Trig Function from an Equation (and Graphing Mixed Review)

13) Writing Sine and Cosine Functions

14) Graphing Secant & Cosecant Functions

15) Graphing Tangent & Cotangent Functions

16) Unit Circle and Graphing Trig Functions Review

17) Unit Circle Cumulative Review WS

Common Core Standard: Functions: Trigonometric Functions

  • Extend the domain of trigonometric functions using the unit circle:
    • A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
    • A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
    • A.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π - x in terms of their values for x, where x is any real number.
  • Model periodic phenomena with trigonometric functions:
    • B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.