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Course summary. Trigonometry with right triangles. Introduction to the trigonometric ratios : Trigonometry with right triangles Solving for a side in a right triangle using the trigonometric ratios : Trigonometry with right triangles Solving for an angle in a right triangle using the trigonometric ratios : Trigonometry with right triangles Modeling with right triangles : Trigonometry with right triangles.

Trigonometric ratios and similarity : Trigonometry with right triangles Sine and cosine of complementary angles : Trigonometry with right triangles Trigonometric ratios of special triangles : Trigonometry with right triangles Introduction to the Pythagorean trigonometric identity : Trigonometry with right triangles The reciprocal trigonometric ratios : Trigonometry with right triangles. Trigonometry with general triangles. The law of sines : Trigonometry with general triangles The law of cosines : Trigonometry with general triangles Solving general triangles : Trigonometry with general triangles.

The unit circle definition of sine, cosine, and tangent. Introduction to radians : The unit circle definition of sine, cosine, and tangent The unit circle definition of sine, cosine, and tangent : The unit circle definition of sine, cosine, and tangent The graphs of sine, cosine, and tangent : The unit circle definition of sine, cosine, and tangent.

Basic trigonometric identities : The unit circle definition of sine, cosine, and tangent Trigonometric values of special angles : The unit circle definition of sine, cosine, and tangent The Pythagorean identity : The unit circle definition of sine, cosine, and tangent Long live Tau : The unit circle definition of sine, cosine, and tangent.

Graphs of trigonometric functions. The graphs of sine, cosine, and tangent : Graphs of trigonometric functions Introduction to amplitude, midline, and extrema of sinusoidal functions : Graphs of trigonometric functions Finding amplitude and midline of sinusoidal functions from their formulas : Graphs of trigonometric functions.

Period of sinusoidal functions : Graphs of trigonometric functions Graphing sinusoidal functions : Graphs of trigonometric functions Constructing sinusoidal functions : Graphs of trigonometric functions.

Trigonometric equations and identities. The inverse trigonometric functions : Trigonometric equations and identities Solving basic sinusoidal equations : Trigonometric equations and identities Solving advanced sinusoidal equations : Trigonometric equations and identities.

Solving sinusoidal models : Trigonometric equations and identities Introduction to the trigonometric angle addition identities : Trigonometric equations and identities Using trigonometric identities to solve problems : Trigonometric equations and identities Challenging trigonometry problems : Trigonometric equations and identities. Course challenge. Review articles. Trig unit circle review The unit circle definition of sine, cosine, and tangent.

Laws of sines and cosines review Solving general triangles. Pythagorean identity review The Pythagorean identity.

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Midline, amplitude, and period review Period of sinusoidal functions. Trigonometric ratios review The reciprocal trigonometric ratios. Get Started Introduction to the trigonometric ratios. Community questions.Whether the angle is positive or negative determines the direction.

A positive angle is drawn in the counterclockwise direction, and a negative angle is drawn in the clockwise direction. Linear speed is a measurement found by calculating distance of an arc compared to time. Angular speed is a measurement found by calculating the angle of an arc compared to time. The tangent of an angle is the ratio of the opposite side to the adjacent side. For example, the sine of an angle is equal to the cosine of its complement; the cosine of an angle is equal to the sine of its complement.

Coterminal angles are angles that share the same terminal side. Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4. Skip to Content. Algebra and Trigonometry Chapter 7.

Table of contents. Answer Key. Try It 7. About 52 ft. The unit circle is a circle of radius 1 centered at the origin. The sine values are equal. Review Exercises 1. Practice Test 1.

### Geometry Chapter 7: Right Triangles And Trigonometry

Previous Next. We recommend using a citation tool such as this one.High school Trigonometry classes introduce students to various trigonometric identities, properties, and functions in detail. Students typically take Trigonometry after completing previous coursework in Algebra and Geometry, but before taking Pre-Calculus and Calculus. Information students learn in Trigonometry helps them succeed in later higher-level mathematics courses, as well as in science courses like Physics, where trigonometric functions are used to model certain physical phenomena.

Trigonometry in particular investigates trigonometric functions, and in the process teaches students how to graph sine, cosine, secant, cosecant, tangent, cotangent, arcsin, arccos, and arctan functions, as well as how to perform phase shifts and calculate their periods and amplitudes.

Trigonometric operations are also discussed, and students also learn about trigonometric equations, including how to understand, set up, and factor trig equations, how to solve individual trigonometric equations, as well as systems of trigonometric equations, how to find trig roots, and how to use the quadratic formula on trigonometric equations. Trigonometric identities are also discussed in Trigonometry classes; students learn about the sum and product identities, as well as identities of inverse operations, squared trigonometric functions, halved angles, and doubled angles.

Students also learn to work with identities with angle sums, complementary and supplementary identities, pythagorean identities, and basic and definitional identities. Another major part of Trigonometry is learning to analyze specific kinds of special triangles.

Students learn to determine angles and side lengths in and right triangles using the law of sines and the law of cosines, as well as how to identify similar triangles and determine proportions using proportionality.

Trigonometry also teaches students about the unit circles and radians, focusing on how to convert degrees into radians and vice versa. Complementary, supplementary, and coterminal angles are all discussed. This focus on angles in the unit circle is also applied to the coordinate plane when angles in different quadrants are examined.

As may now be apparent, many students find themselves very apprehensive about taking, and keeping up with, a Trigonometry course. Each Trigonometry Practice Test features a dozen multiple-choice Trigonometry questions, and each question comes with a full step-by-step explanation to help students who miss it learn the concepts being tested.

Questions are organized in Practice Tests, which draw from various topics taught in Trigonometry; questions are also organized by concept. So, if a student wants to focus on only answering questions about using the law of sines, questions organized by concept makes this possible. We are open Saturday and Sunday!

Subject optional. Home Embed. Email address: Your name:. Take the Varsity Learning Tools free diagnostic test for Trigonometry to determine which academic concepts you understand and which ones require your ongoing attention.

Each Trigonometry problem is tagged down to the core, underlying concept that is being tested.Choose your answers to the questions and click 'Next' to see the next set of questions.

You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results.

Start Exam. Page 1 Question 1 1. Find the value of x, rounded to the nearest tenth. Question 2 2. The Pythagorean Theorem is a special case of what? Question 3 3.

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If two sides of a right triangle measures 6 and 8 inches, what does the hypotenuse measure? Question 4 4. If the hypotenuse of a triangle is 31, approximately how long is the leg?Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter?

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### Chapter 7: Right Triangles and Trigonometry Chapter Exam

Find a degree that fits your goals. Exam Instructions: Choose your answers to the questions and click 'Next' to see the next set of questions. Answered 0 of 30 questions. Start Exam. Page 1 Question 1 1. If the hypotenuse of a triangle is 18, approximately how long is the short leg? Question 2 2. If side a is 34 units long, approximately how long is side b? Question 3 3.

A right triangle has one leg that measures 13 centimeters, and the hypotenuse is 17 centimeters. How long is the missing leg? Question 4 4.

Find the value of x, rounded to the nearest tenth. Question 5 5. What is the trigonometric ratio for cosine? Page 2 Question 6 6. If side a is 84 units long, approximately how long is side b?

## Glencoe Geometry Chapter 7: Right Triangles and Trigonometry Chapter Exam

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