In these lessons, we will look at how to find the Maximum and Minimum Values of Sine and Cosine Functions.

**Maximum and Minimum Values of Sine and Cosine Functions**

How to find the maximum and minimum values of sine and cosine functions with different coefficients?

Example 1:

Find the maximum value and minimum value for the functions:

a) y = 6sin(7x)

b) y = -1/2 cos(3πx)

**How to find the maximum and minimum values and zeros of sine and cosine?**

A 'word problem' and how to find the maximum value of a cosine function.

Example:

A market research company finds that traffic in a local mall over the course of a day could be estimated by

P(t)= -2000 cos(π/6 t) + 2000

where P is the population and t is the time after the mall opens on hours.

a) How long after the mall opens, does it reach its maximum number of people?

b) What is the maximum number of people?

**How to find the sinusoidal equation given the maximum and minimum points?**

y = A sin b(x - h) + k

y = A cos b(x - h) + k

A = |(max - min)/2|

P = (2π)/|b|

k = (max + min)/2

Example:

Given the following maximum and minimum points find the sine and cosine equations

Max = (π/4, 5)

Min = (π/2, -1)

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

How to find the maximum and minimum values of sine and cosine functions with different coefficients?

Example 1:

Find the maximum value and minimum value for the functions:

a) y = 6sin(7x)

b) y = -1/2 cos(3πx)

A 'word problem' and how to find the maximum value of a cosine function.

Example:

A market research company finds that traffic in a local mall over the course of a day could be estimated by

P(t)= -2000 cos(π/6 t) + 2000

where P is the population and t is the time after the mall opens on hours.

a) How long after the mall opens, does it reach its maximum number of people?

b) What is the maximum number of people?

y = A sin b(x - h) + k

y = A cos b(x - h) + k

A = |(max - min)/2|

P = (2π)/|b|

k = (max + min)/2

Example:

Given the following maximum and minimum points find the sine and cosine equations

Max = (π/4, 5)

Min = (π/2, -1)

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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