About This Chapter
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- Begin your preparation for the NY Regents integrated algebra exam.
- Identify the introductory trigonometry concepts that you're stuck on.
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This chapter of our NY Regents Exam - Integrated Algebra tutoring solution will benefit any student who is trying to learn the basics of trigonometry and earn passing scores on the exam. This resource can help students including those who:
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- Learn at Your Pace: You can pause and rewatch lessons as often as you'd like, until you master the material.
- Learn how to solve trigonometric problems that include sine and cosine.
- Become familiar with the Law of Sines and Law of Cosines.
- Graph tangent functions.
- Calculate slopes and tangents.
- Understand how to graph sine and cosine transformations.
- Memorize the first quadrant of the unit circle.
- List the properties of right triangles.
- Identify the different types of right triangles.
- Take a look at the double angle formula.
- Convert between radians and degrees.
- Solve trigonometric equations for x.
- Discuss the 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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- NY Regents - Sets: Tutoring Solution
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- NY Regents - Working with Data: Tutoring Solution
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