Understanding Amplitude and Phase Shift

This video tutorial teaches how to graph sine and cosine functions using transformations. It covers the unit circle, amplitude, period, phase shift, and vertical shift. The video provides four examples, demonstrating step-by-step how to apply transformations to graph sine and cosine functions effectively.

What is the primary focus of this video tutorial?

• Solving quadratic equations

• Graphing sine and cosine functions

• Graphing linear equations

• Understanding logarithms

In the unit circle, what does the y-coordinate represent?

• Tangent value

• Sine value

• Cosine value

• Cotangent value

What does the coefficient in front of sine or cosine represent?

• Period

• Amplitude

• Phase shift

• Vertical shift

In the function y = 2 sin(1/2 x + π) - 1, what is the amplitude?

• 1

• 2

• 1/2

• π

For the function y = 3 cos(2(x - π/4)) + 1, what is the phase shift?

• Left π/4

• Right π/4

• Left π

• Right π

What effect does a negative sign in front of the sine function have?

• Increases amplitude

• Reflects over the x-axis

• Shifts graph up

• Shifts graph down

In the function y = 1/2 cos(1/4 x - 2π) + 1, what is the vertical shift?

• Up 1

• Down 1

• Up 2

• Down 2