# 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.

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:
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 with step-by-step solutions
Right Triangle Trigonometry, Radian Measure and Circular Functions,
Graphing Trigonometric Functions, Simplifying Trigonometric Expressions,
Verifying Trigonometric Identities, Solving Trigonometric Equations,
Complex Numbers, Analytic Geometry in Polar Coordinates,
Exponential and Logarithmic Functions, Vector Arithmetic, Vectors

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