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Transformation of trigonometric functions

Trigonometry: Master Angles, Ratios & Functions

Right Triangle Trigonometry

Use sine ratio to calculate angles and sides (Sin = \(  \frac{o}{h}\) )

Use cosine ratio to calculate angles and sides (Cos =  \(  \frac{a}{h}\)  )

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

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Solving expressions using 45-45-90 special right triangles 

Solving expressions using 30-60-90 special right triangles 

Use tangent ratio to calculate angles and sides (Tan =  \(  \frac{o}{a}\)  )

Trigonometric Ratios and Angle Measures

Unit circle

Area of triangles:\(\frac{1}{2} ab\) sinC

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

Graphing Trigonometric Functions

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

Applications of Trigonometry Functions

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

Trigonometric Identities

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Cofunction identities

Trigonometric Equations

Solving first degree trigonometric equations

Solving second degree trigonometric equations

Solving trigonometric equations involving multiple angles

Determining non-permissible values for trig expressions

Solving trigonometric equations using pythagorean identities

Solving trigonometric equations using Pythagorean identities

Solving trigonometric equations using sum and difference identities

Solving trigonometric equations using double-angle identities

Inverse Trigonometric Functions

Finding inverse trigonometric function from its graph

Evaluating inverse trigonometric functions

Finding inverse reciprocal trigonometric function from its graph

Finding exact value of inverse reciprocal trig functions

Inverse Reciprocal Trigonometric Function: Finding the Exact Value

Inverse reciprocal trigonometric function: finding the exact value

Bearings

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

math

<h2>What is Trigonometry?</h2>
Trigonometry is an aspect of mathematics that studies the lengths and angles of triangles. It&apos;s most commonly associated with planar right-angle triangles that contain one 90-degree angle. An understanding of trigonometry is required across a variety of industries, from science and engineering, to construction and even video games!
As you study the subject, you&apos;ll develop your knowledge of triangles and how they are broken down into 3 sections, the adjacent, the opposite, and the hypotenuse. You&apos;ll use these sections of the triangle to find the values of Sine, Cosine, and Tangent (or Sin, Cos, Tan). These are the main functions within trigonometry and put simply, they are calculated dividing one side of the right-angled triangle with another.
A prerequisite for trigonometry courses tends to be either <a href='[[region_textbook.html|{"textbook_key":"algebra-1"}]]'>Algebra 1</a> or <a href='[[region_textbook.html|{"textbook_key":"algebra-2"}]]'>Algebra 2</a>. Additionally, trig courses are best pursued after you have built a solid foundation of knowledge within statistics. Once you have completed your trig courses, you could then go on to study <a href='[[region_textbook.html|{"textbook_key":"pre-calculus"}]]'>Precalculus</a> or <a href='[[region_textbook.html|{"textbook_key":"calculus"}]]'>Calculus 1</a>.
Throughout your lessons in trigonometry, you&apos;re bound to cover the following topics:
<ul type="disc">
<li>Trigonometric ratios</li>
<li>CSC (cosecant) math</li>
<li>Right triangle trigonometry</li>
<li>Reference triangles</li>
<li>Applications of trigonometry</li>
</ul>
If you&apos;re looking to build your knowledge surrounding trig rules and principles, our online <a href='[[canon_textbook.html|{"textbook_key":"trigonometry"}]]'>trigonometry videos</a> and revision materials will help you tackle every aspect of trig. We&apos;ve got expert lecturers that have worked to build valuable content that covers all areas of trigonometry, areas that you&apos;d would expect to find in modern textbooks and taught in today&apos;s classrooms.
Sign-up for a StudyPug subscription and you&apos;ll have unlimited access to all our math content, allowing you to build your understanding of the prerequisite courses, trig courses, and then the follow-up <a href="[[canon_textbook.html|{"textbook_key":"calculus-help"}]]">calculus</a> courses.
As mentioned above, we have videos from trig experts, covering all the content you&apos;re currently being taught at school/college. Our trigonometry videos will provide you with an Introduction to trigonometry, expanding your understanding of the basic elements and progressing to the more complex areas of trigonometry.

<h2>What Does Adjacent Mean?</h2>
The word adjacent means "next to or adjoining something else". Within trigonometry, the adjacent refers to the side of the triangle next to or adjoining the right-angle. The other side next to the angle is referred to as the hypotenuse and the side opposite the adjacent is referred as the "opposite side".
Using the adjacent side of a triangle, you can find the value of both cos and tan. To find cos, divide it with the hypotenuse, and to find tan, divide it by the opposite side of the triangle.

<h2>Is Trigonometry Hard?</h2>
If you&apos;ve taken a brief glance at trigonometry without context, it&apos;s easy to see why you might feel like its unapproachable or tough to get your head around. The truth is, it&apos;s not that hard once you have a firm understanding of the underlying principles of trig. Developing an understanding of Sin, Cos, Tan will allow you to tackle trigonometry with relative ease.
If you want trigonometry help or a study aide for your trig lessons, our online trigonometry tutorials will walk you through all the topics related to trig and the questions that are bound to come up on your exams. Topics like the unit circle, trigonometric identities, trigonometric functions, right triangle trigonometry, trigonometric equations, and more.
Outside of the classroom, broaden your understanding of the core concepts of trig with our fantastic tutorials that show you easy to understand solutions to even the hardest trigonometry problems. Furthermore, you can reinforce the knowledge you&apos;ve built with our trigonometry practice materials.
Our content has been designed by experienced trigonometry teachers and we cover all the topics you&apos;d find in current textbooks like <a href="https://books.google.ca/books?id=oc9uCgAAQBAJ&pg=PP4&lpg=PP4&dq=brooks+cole+McKeague+trigonometry&source=bl&ots=GGqIHXnvDG&sig=IyZJ6lkM9tHazsub075g1Y5u6vc&hl=en&sa=X&ved=0ahUKEwjumZKSl-HRAhUK7GMKHdOSAN4Q6AEIRjAH#v=onepage&q=brooks%20cole%20McKeague%20trigonometry&f=false">Trigonometry McKeague</a>, <a href="http://www.pearsonschool.com/index.cfm?locator=PS1lMi&PMDbProgramID=115981&elementType=attribute&elementID=1">Blitzer Algebra and Trigonometry</a>, and <a href="https://www.pearsonhighered.com/product/Lial-Trigonometry-10th-Edition/9780321671776.html">Algebra 2 and Trigonometry Lial</a>.
At StudyPug, we understand that the way you learn trigonometry may be different to everyone else. With that in mind, we have built our platform with a "trigonometry for dummies" approach that starts from the ground up, assumes no prior knowledge, and covers all areas of the subject matter. Each section of our content has also been thoughtfully designed to flow naturally from one area to the next, allowing you to build off what you&apos;ve just learned, introducing more complex elements when you&apos;re ready.
If you choose to subscribe to our trigonometry content, you&apos;ll have direct access to every lesson on our site. If you&apos;re looking for help with specific sections of trigonometry, we&apos;ve got you covered. Furthermore, there&apos;s no need to study topics you&apos;re already familiar with. You can customize each session with the content that is relevant to you.
Put simply, trigonometry tutorials and revision doesn&apos;t have to be hard. If you want to learn trigonometry, StudyPug can help. Whether you need help with trigonometry questions or if you have trigonometry homework to complete, StudyPug delivers a host of online videos, exam prep materials, and additional resources that can dramatically improve your understanding of the subject and better prepare you for upcoming exams.

<h2>What is Sin Cos Tan?</h2>
Sin, Cos, Tan, or Sine, Cosine and Tangent are the three basic trig functions. They related to the ratios of each side of a right-angle triangle. Understanding sin, cos, tan, is vital to understanding trigonometry. Below is how each one is calculated.
<ul type="disc">
<li>Sin (S) &ndash; Opposite (O) divided by Hypotenuse (H) - SOH</li>
<li>Cos (C) &ndash; Adjacent (A) divided by Hypotenuse (H) - CAH</li>
<li>Tan (T) &ndash; Opposite (O) divided by Adjacent (A) - TOA</li>
</ul>
To help you remember this, think of SOHCAHTOA. To help you further, we have an extensive collection of revision materials to help make interpreting the information easier.

<h2>How to Learn Trigonometry?</h2>
With trigonometry, much like everything in math, practice makes perfect. Reviewing what you&apos;ve been taught in the classroom will help you to digest and retain the information. It&apos;s also a good way of highlighting areas of weakness, allowing you to build out more effective revision strategies. Revise the areas you&apos;re unsure of and set aside some time after school/college to test yourself. This will allow you to track your progress and will help to build your confidence ahead of your exams.
We understand that getting yourself into a good study habit is easier said than done. If you find it hard to focused when it comes to studying, you&apos;re not alone. That&apos;s why we at StudyPug offer our students easy to follow step-by-step examples that breakdown the complex language. Our students use our platform for their Trigonometry exam prep and for additional Trigonometry homework help. We&apos;re their all in one trigonometry tutor.
Our easy practice trig materials and online videos are available 24/7 and as our content is delivered via video, you can manually pause, rewind, or fast-forward the information, allowing you to skip pieces that are not relevant to you and learn at your own pace. We find that a lot of our students prefer the video format as the content is delivered in a conversational way that&apos;s easier to follow than traditional textbooks.
To get you started on the path to understanding trigonometry basics, our trigonometry tutoring platform has a collection of free lessons across the following subject areas:
<ul type="disc">
<li>Right Triangle Trigonometry</li>
<li>Ratios and Angle Measure</li>
<li>Trigonometric Identities</li>
<li>Solving Trigonometric Equations</li>
<li>Imaginary and Complex Numbers</li>
</ul>
Explore our free content and review our customer feedback section to see how our study platform has helped many students just like you find easy and reliable trig help. For additional help, check out our <a href="https://www.studypug.com/blog/8-secrets-to-better-marks-in-math/">tips for achieving better math marks</a> today!

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-trigonometry.png

Ex. 1:

Ex. 2:

Graphing a negative tangent function with horizontal shift and period change

Graphing a transformed sine function and finding its key properties

Graphing a transformed secant function using the cosine method

Graphing a negative sine function with transformations

After learning all the graphs of basic trigonometric functions, in this lesson, we are going to go a little bit further on how the graphs will be transformed as the functions change. The general form for the equation of trig functions is y = f [B(x + c)] + D, where f refers the trig function; A refers to the amplitude/steepness; B represents the period of the graph; C refers to phase shift (left or right) and D represents vertical shift (up or down). We will learn how to graph the trig function for multiple periods; state the vertical displacement, phase shift, period and amplitude; and also find the domain and range of the transformed functions.

Combining transformations of functions