Problem 3 Finding the Amplitude of a Sine Curve

The graphing calculator screens show four graphs of y = a sin x . y equals eh sine x .  Each x-axis shows values from 0 to 2π.

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1. What is the amplitude of each sine curve? How does the value of a affect the amplitude?

   The amplitude of y = sin x y equals sine x  is 1, and the amplitude of y = 2 sin x y equals 2 sine x  is 2.

   The amplitude of y = − sin x y equals negative sine x  is 1, and the amplitude of y = − 2 sin x y equals negative 2 sine x  is 2.

   In each case, the amplitude of the curve is | a | . vertical line eh vertical line .

   Think

   What is the amplitude?

   The amplitude is half the difference of the maximum and minimum values of the periodic function.

2. How does a negative value of a affect the position of the curve?

   When a is negative, the graph is a reflection across the x-axis.

✓ Got It?

3. The equation of the graph is of the form y = a sin x . y equals eh sine x .  What is the amplitude of the sine curve? What is the value of a?
   1. 
   2. 

Take Note Concept Summary: Properties of Sine Functions

Suppose y = a sin b θ , y equals eh sine b theta comma  with a ≠ 0 , b > 0 , eh not equal to 0 comma b greater than 0 comma  and θ in radians.

• | a | absolute value of eh ,  is the amplitude of the function.
• b is the number of cycles in the interval from 0 to 2 π . 2 pi .
• 2 π b fraction 2 pi , over b end fraction  is the period of the function.