Graphing Trigonometric Functions

Period of Sin/Cos Equation

2π/B

Phase Shift of Sin/Cos Equation

BX +- C = 0

Sin Form

y = +-A * Sin (BX +- C) +- D

Cos Form

y = +-A * Cos (BX +- C) +- D

Meaning of A, B, C, and D in Sin/Cos Form?

A: Amplitude

B: Scale

C: Phase Shift

D: Vertical Shift

Shape of + Sin Equation?

Shape of - Sin Equation?

Shape of + Cos Equation?

Shape of - Cos Equation?

Steps to Graphing Sin/Cos (9)

1. Collect Information:

   1. (A) Amplitude

   2. (B) Scale

   3. (C) Phase Shift

   4. (D) Vertical Shift

2. Phase Shift

3. Period (Add Phase shift if present)

4. Step (same as Phase Shift)

5. Plot Graph (Divide Initial Period / 4)

6. Draw Graph

Shape of + Tan Equation?

Shape of - Tan Equation? 

Asymptotes of Tan Function

-π/2 < BX +- C < π/2

Period for Tan/Cot

π/B

Steps for Graphing Tan (6)

1. Collect Information:

   1. (A) Amplitude

   2. (B) Scale

   3. (C) Phase Shift

   4. (D) Vertical Shift

2. Find/Draw (ASM) Asymptotes

3. Find Period (if graphing multiple periods)

4. Plot Center Point of Graph (ASM/2,D)

5. Plot 2 other Points (X,+-A)

6. Draw

Shape of + Cot Equation?

Decreasing Function (Down Left to Right)

Shape of - Cot Equation?

Same as + Tan Function

Asymptotes of Cot Function

0 < BX +- C < π