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More Lessons for High School Regents Exam

Math Worksheets

High School Math based on the topics required for the Regents Exam conducted by NYSED.

The following diagram shows how to transform sine and cosine graphs. Scroll down the page for more examples and solutions on how to graph sine and cosine functions.

**Graphing Sine and Cosine With Different Coefficients (Amplitude and Period)**

Examples:

State the amplitude and period of each of the following functions.

a) y = -4 cos (3x)

b) y = 1/2 sin x

c) y = √2 cos(1/2 x)

**Trigonometric Functions and Graphing: Amplitude, Period, Vertical and Horizontal Shifts**

Examples:

Graph y = 2 cos (x - π/2) + 1**Graphing Sine and Cosine with Phase (Horizontal) Shifts**

Examples:

What is the phase shift for each of the following functions

a) y = cos(x - 4)

b) y = sin (2(x + 1))

c) y = cos(10x + 30)**An Introduction to the Graphs of Sine and Cosine Functions**

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.

More Lessons for High School Regents Exam

Math Worksheets

High School Math based on the topics required for the Regents Exam conducted by NYSED.

The following diagram shows how to transform sine and cosine graphs. Scroll down the page for more examples and solutions on how to graph sine and cosine functions.

Examples:

State the amplitude and period of each of the following functions.

a) y = -4 cos (3x)

b) y = 1/2 sin x

c) y = √2 cos(1/2 x)

Examples:

Graph y = 2 cos (x - π/2) + 1

Examples:

What is the phase shift for each of the following functions

a) y = cos(x - 4)

b) y = sin (2(x + 1))

c) y = cos(10x + 30)

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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