# Maximum and Minimum Values of Sine and Cosine Functions

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

Related Topics:
More Lessons for Trigonometry
Math Worksheets

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) Trigonometry Calculator
Right Triangle Trigonometry
Graphing Trigonometric Functions
Simplifying Trigonometric Expressions
Verifying Trigonometric Identities
Verifying Trigonometric Identities
Using Fundamental Identities
Solving Trigonometric Equations
Complex Numbers
Analytic Geometry in Polar Coordinates
Exponential and Logarithmic Functions
Vector Arithmetic
Vectors

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.