Graphing Sine and Cosine Functions

What functions are related to angles?

• Exponential functions

• Logarithmic functions

• Trigonometric functions

• Polynomial functions

What does the amplitude of a trigonometric function represent?

• The vertical stretch or compression

• The period of one complete cycle

• The horizontal shift of the function

• The height from the middle point to the peak

How is the period of a trigonometric function defined?

• The distance from one peak to another

• The vertical shift of the function

• The amplitude of the function

• The phase shift of the function

What does a phase shift in a trigonometric function indicate?

• A horizontal shift of the function

• A change in period

• A change in amplitude

• A vertical shift of the function

What theorem helps determine the amplitude and period of a sine or cosine function?

• Euler's formula

• The theorem on phase shifts

• The theorem on amplitudes and periods

• The Pythagorean theorem

How do you find the amplitude of a function like y = a * sin(bx)?

• 2π / |b|

• |a|

• -c / b

• |b|

What is the correct formula to find the period of a trigonometric function?

• |b|

• 2π / |b|

• |a|

• 2π / |a|

In the function y = a * sin(bx + c) + d, what does 'd' represent?

• Vertical shift

• Phase shift

• Period

• Amplitude

How can you determine the phase shift of a trigonometric function?

• 2π / |a|

• -c / b

• 2π / |b|

• |a|

What does the graph of y = 2 sin(3x) demonstrate about amplitude and period?

• Amplitude of 3 and period of 2π/2

• Amplitude of 3 and period of π/2

• Amplitude of 2 and period of 2π/3

• Amplitude of 2 and period of 3π/2