Trigonometric Functions and Their Shifts

The video tutorial explains how trigonometric functions can be shifted vertically and horizontally. It introduces the six basic trigonometric functions and describes how to identify and apply phase and vertical shifts. The tutorial provides examples of phase shifts in sine and cosine functions and a vertical shift in a cosine function. It concludes with a summary of how to use the components of a function to achieve these shifts.

What are the six basic trigonometric functions?

• Sine, Cosine, Tangent, Secant, Cosecant, Cotangent

• Sine, Cosine, Tangent, Arctangent, Arcsine, Arccosine

• Sine, Cosine, Tangent, Cotangent, Arcsine, Arccosine

• Sine, Cosine, Tangent, Arctangent, Secant, Cosecant

Which component of a trigonometric function represents its amplitude?

• B

• C

• A

• D

What does the constant C in a trigonometric function indicate?

• Phase Shift

• Frequency

• Amplitude

• Vertical Shift

If a sine function is given as y = sin(x - π/4), how does the graph shift?

• Down π/4 units

• Up π/4 units

• Right π/4 units

• Left π/4 units

In the function y = cos(x + π/2), what is the phase shift?

• Down π/2 units

• Up π/2 units

• Left π/2 units

• Right π/2 units

How does the graph of y = cos(x - 6) shift?

• Right 6 units

• Left 6 units

• Up 6 units

• Down 6 units

What does the value of D in a trigonometric function determine?

• Frequency

• Amplitude

• Phase Shift

• Vertical Shift

Which formula component is used to shift trigonometric functions vertically?

• D

• C

• B

• A

When B equals one, which value is used to move the graph left and right?

• C

• D

• B

• A

What is the effect of a positive phase shift on a trigonometric function?

• Shifts the graph upwards

• Shifts the graph to the right

• Shifts the graph downwards

• Shifts the graph to the left