Trigonometric Graphs & Transformations

Presentation

•

Mathematics

•

11th - 12th Grade

•

Hard

Atul Moksin

Used 16+ times

FREE Resource

17 Slides • 6 Questions

Trigonometric Graphs & Transformations

Sketching a graph and how to transform them

Basic Trigonometric Graphs

$y=\sin x\$
$y=\cos\ x$
$y=\tan x$

This is a graph of $y=\sin x$ for $-90\degree\le x\le360\degree$

What about the others? How do they look like?

Your turn

Try all equations you can think of.

Enter the equations in the following website, and explore.

Don't forget to click on autoscale in settings.

Multiple Choice

When $y=\sin x$ is transformed into $y=2+\sin\ x$ , what happens to the graph?

Graph is shifted downwards by 2 units

Graph is stretched by 2 units, parallel to the y-axis

Graph is shifted upwards by 2 units

Graph is stretched by 2 units, parallel to the x-axis

Try again with Autograph

Explore what happens to the graph when you add or minus a constant.

Multiple Choice

When $y=\sin x$ is transformed into $y=-\sin\ x$ , what happens to the graph?

Graph is reflected in the y-axis

Graph is shifted upwards by 1 unit

Graph is reflected in the x-axis

Graph is stretched by a factor of 2, parallel to the x-axis

Try again with Autograph

Explore what happens to the graph when you it becomes negative.

Multiple Choice

When $y=\sin x$ is transformed into $y=2\sin\ x$ , what happens to the graph?

Graph is stretched by a factor of $\frac{1}{2}$ , parallel to the y-axis

Graph is stretched by a factor of $\frac{1}{2}$ , parallel to the x-axis

Graph is stretched by a factor of 2, parallel to the y-axis

Graph is stretched by a factor of 2, parallel to the x-axis

Multiple Choice

When $y=\tan x$ is transformed into $y=\tan2\ x$ , what happens to the graph?

Graph is stretched by a factor of $\frac{1}{2}$ , parallel to the y-axis

Graph is stretched by a factor of $\frac{1}{2}$ , parallel to the x-axis

Graph is stretched by a factor of 2, parallel to the y-axis

Graph is stretched by a factor of 2, parallel to the x-axis

Try again with Autograph

Explore what happens to the graph when you multiply the function or the x in the function with a factor e.g. $y=\cos\ \frac{1}{2}x$

Multiple Choice

When $y=\sin x$ is transformed into $y=\sin\ \left(x+30\right)\degree$ , what happens to the graph?

Graph is shifted by $30\degree$ to the left

Graph is shifted by $30\degree$ to the right

Graph is shifted by $30\degree$ upwards

Graph is shifted by $30\degree$ downwards

Try again with Autograph

Explore what happens to the graph when you add or minus an angle from the x function e.g. $y=\tan\ \left(x-45\right)\degree$

In summary:

$y=f\left(x\right)+a$ : Graph shifts upwards (downwards when minus) by a units.
$y=af\left(x\right)$ : Graph stretches by factor a, parallel to y-axis
$y=f\left(ax\right)$ : Graph stretches by a factor of $\frac{1}{a}$ , parallel to the x-axis
$y=f\left(x+c\degree\right)$ : Graph shifts to the left (right when minus) by $c\degree$
$y=-f\left(x\right)$ : Graph is reflected in the y-axis.

Take a look at this image carefully.

Take note of where the curve cuts the x-axis and y-axis. It is also helpful to note the maximum and minimum values.

The next slide, will require you to answer from this graph.

Multiple Choice

What is the equation of this graph?

$y=3\sin\left(x+60\right)\degree$

$y=3\cos\left(2x+60\right)\degree$

$y=2\sin\left(3x+60\right)\degree$

$y=3\sin\left(2x-60\right)\ \degree$

Homework!

Take a screenshot of a trigonometric equation you tried on Autograph.

Be creative.

Make it as complicated as you want.

Send the screenshot to our groupchat when you're done.

Trigonometric Graphs & Transformations

Sketching a graph and how to transform them

Show answer

Auto Play

Slide 1 / 23

SLIDE

Similar Resources on Wayground

17 questions

Least Squares Regression Line Practice

Presentation

•

12th Grade

20 questions

Reading Graphs

Presentation

•

11th Grade

20 questions

Negative Exponents

Presentation

•

12th Grade

20 questions

Persamaan Lingkaran

Presentation

•

11th Grade

20 questions

Graphing Polynomials

Presentation

•

11th Grade

14 questions

Graphing Sine and Cosine Functions

Presentation

•

11th - 12th Grade

18 questions

Basic Probability

Presentation

•

11th - 12th Grade

20 questions

5.3 Dot Plots

Presentation

•

11th - 12th Grade

Popular Resources on Wayground

10 questions

Safety Day 2026 – Student Review

Quiz

•

9th Grade

21 questions

Continents and Oceans

Quiz

•

6th Grade

20 questions

Parts of Speech

Quiz

•

5th Grade

16 questions

Subject & Predicate

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

12 questions

Map Skills

Quiz

•

3rd Grade

22 questions

Continents and Oceans

Quiz

•

5th Grade

15 questions

Rounding Decimals

Quiz

•

5th Grade

Discover more resources for Mathematics

12 questions

Identify Rigid Transformations

Quiz

•

8th - 12th Grade

10 questions

Complementary, Supplementary, Vertical, and Linear Pairs

Quiz

•

9th - 12th Grade

22 questions

Identify Vertical and Horizontal Translations

Quiz

•

9th - 12th Grade

10 questions

Graphing Inequalities on a Number Line

Quiz

•

9th - 12th Grade

17 questions

Identifying Parallel And Perpendicular Lines

Quiz

•

9th - 12th Grade

18 questions

Integer Operations

Quiz

•

5th - 12th Grade

18 questions

Parallel lines cut by a transversal

Quiz

•

9th - 11th Grade

14 questions

Evaluate Linear Functions and Their Applications

Quiz

•

9th - 12th Grade