About This Chapter
Who's it for?
Anyone who needs help learning or mastering integrated algebra material will benefit from taking this course. There is no faster or easier way to learn integrated algebra. Among those who would benefit are:
- Students who have fallen behind in understanding sine and cosine or working with slopes and tangents on a graph
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about introductory trigonometry
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How it works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Intro to Trigonometry chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Intro to Trigonometry chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any introductory trig question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
This chapter helps students review the concepts in an Intro to Trigonometry unit of a standard integrated algebra course. Topics covered include:
- Laws of sines and cosines
- Graphing the tangent function
- Slopes and tangents on a graph
- Graphing sine and cosine transformations
- Converting between radians and degrees
- Basic trig identities
1. Trigonometry: Sine and Cosine
Sine and cosine are basic trigonometric functions that are used to solve for the angles and sides of triangles. Review trigonometry concepts and learn about the mnemonic used for sine, cosine, and tangent functions.
2. Law of Sines: Definition and Application
Law of Sines, also known as sine law or sine rule, is an equation relating the sines of the three angles of a triangle to its three sides. Learn about the definition of the Law of Sines and understand how to apply it by completing math problems involving triangles.
3. Law of Cosines: Definition and Application
The law of cosines is an equation that considers the two known sides of a triangle and the cosine of one of its known angles to find the one missing side. Explore the definition and application of the law of cosines and learn how to solve problems involving triangles through the given practice problems.
4. Graphing the Tangent Function: Amplitude, Period, Phase Shift & Vertical Shift
Unlike other trigonometric functions, a tangent function can be transformed in four different ways. Learn how to graph the tangent function and to visualize and change the amplitude, period, phase shift, and vertical shift of a tangent function.
5. Slopes and Tangents on a Graph
In mathematics, slopes and tangents help determine ratios and rates of change. Learn how to show slopes and tangents as lines on a graph, explore the concept of slope as it pertains to hills, and recognize how slope can be used to describe steepness.
6. Graphing Sine and Cosine Transformations
The sine and cosine signal waveforms, or waves, can be transformed in multiple ways. Learn how to identify the three types of sine and cosine transformations, including amplitude, period, and phase shift, and practice graphing the transformations with sample problems.
7. Unit Circle: Memorizing the First Quadrant
Memorizing the unit circle allows for calculation of its angles' trigonometric values without a calculator. Explore and memorize the unit circle's first quadrant, including its main points, and its sine, cosine, and tangent values.
8. Properties of Right Triangles: Theorems & Proofs
A triangle is considered a right triangle when it has a 90-degree angle. Learn the definition and properties of right triangles, and explore relevant proofs and theorems about triangles, such as the Pythagorean theorem and the right triangle altitude theorem.
9. Special Right Triangles: Types and Properties
There are two types of special right triangles that have either 30-60-90 degree angles or 45-45-90 degree angles. Learn more about the definitions and explore the properties of 30-60-90 and 45-45-90 degree angles of special right triangles through examples.
10. The Double Angle Formula
In trigonometry, a double angle is twice as large as a common angle. Learn how to calculate the double angle formula, explore trigonometry twins for sine, cosine, and tangent, and apply this information in practice problems using the double angle formula.
11. Converting Between Radians and Degrees
The two most widely used units of measure for angles are degrees and radians. Learn how to convert radians to degrees and degrees to radians using the concepts of proportion and priority.
12. How to Solve Trigonometric Equations for X
Trigonometric functions can be simplified using their inverses and their angles can be solved within their restricted domains. Learn how to solve trigonometric equations for x using inverse operations and based on trigonometric restrictions.
13. List of the Basic Trig Identities
The fundamental trigonometric identities are equations applicable to triangles with a right angle. Discover the trigonometric identities established using sine, cosine, tangent, cotangent, secant, and cosecant functions, and learn their use and applications.
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