Graphing Sine and Cosine Functions (More Challenging Examples)

Ready to tackle more complex sine and cosine graphs? In this video, Mario's Math Tutoring guides you through graphing transformed sinusoidal functions, focusing on equations with horizontal shifts (phase shifts) and factoring out the 'B' value.

You'll learn:

The fundamental shapes of sine (starts at midline) and cosine (starts at maximum) graphs.
Crucial Step: How to factor out the 'B' value from inside the parentheses to correctly identify the horizontal shift.
Calculating the period using the formula Period = 2π / B.
Using the period to set up an appropriate scale for your graph.
Understanding the effects of amplitude ('A') and vertical shift ('K').
How to handle reflections (negative 'A' values).
A visual technique using a "shifted origin" and midline to easily plot transformed graphs.
This tutorial is perfect for trigonometry and pre-calculus students looking to master graphing sine and cosine functions with various transformations.

Timestamps:
00:00 Intro
0:12 How to Graph Basic Sine and Cosine Using the Unit Circle
2:07 Example 1 Graph y=-2sin((1/2)x+pi)-3
3:00 Formula for Finding the Period
4:30 Graph From the Shifted Origin
6:42 Example 2 Graph y=(1/2)cos(4x - pi/2) + 2
8:17 Graph From the Shifted Origin

Related Videos:

Graph Sine and Cosine
   • Graphing Sin and Cos  

Graphing Tan and Cot
   • Graphing Tan and Cot  

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