Changes in Period and Phase Shift of Sine and Cosine Functions — Quiz

Question 10 • Advanced Algebra: Concepts and Connections

What is the general equation of a sine function with an amplitude of 2 , a period of pi and a horizontal shift of pi units?

Answer

y is equal to sine of open paren 2 times open paren x plus pi close paren close paren

y is equal to 2 sine open paren 2 times open paren x minus pi close paren close paren

y is equal to sine of open paren 0 point 5 times open paren x minus pi close paren close paren

y is equal to 2 sine open paren 4 times open paren x plus pi close paren close paren

Explanation

A sine function has the form y = A sin(B(x − C)), where its amplitude is |A| and its period is 2π/|B|. An amplitude of 2 gives A = 2, and a period of π gives |B| = 2π/π = 2. Choice B, y = 2 sin(2(x − π)), has both values and shifts the graph horizontally by π units.

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