About This Chapter
ORELA Math: Trigonometric Functions - Chapter Summary
This chapter offers a number of resources to help you master the trigonometric functions you're expected to know for the ORELA Math certification assessment. Short, engaging lessons break down the following concepts:
- Sine, cosine, cotangent, secant and cotangent
- The Pythagorean theorem and trigonometric ratios
- Applications of unit circles in trigonometry
- Right triangles and special right triangles
- The law of sines and the law of cosines
- The double-angle formula and special angles
Take the quick, multiple-choice self-assessment after each video to see how well you understand the trigonometric functions you've reviewed. If you have any questions or get stuck, let our instructors know you need help.
Objectives of the ORELA Math: Trigonometric Functions Chapter
Questions about calculus and trigonometry make up 19%, or approximately 1/5, of the ORELA certification assessment for math educators. Use this chapter to study the trigonometric functions you're bound to run into on the exam.
You will also be expected to demonstrate mastery in the following four areas: measurement and geometry (making up 19% of the assessment); statistics, probability and discrete math (19%); math processes and number sense (19%); and patterns, algebra and functions (24%). ORELA questions are multiple-choice, as are our lesson quizzes--use them to practice for the exam. You'll have 4 1/4 hours to complete your assessment.
1. Trigonometry: Sine and Cosine
Learn an easy trick to help you solve trigonometry problems, including problems with sine, cosine and inverse trig functions. At the end of this lesson, you'll know what SohCahToa means and how to use it.
2. Trigonometry and the Pythagorean Theorem
Explore how the Pythagorean Theorem can be used in conjunction with trigonometric functions. In this lesson, take an inverse trigonometric function, and define all three sides of a right triangle.
3. Other Trigonometric Functions: Cotangent, Secant & Cosecant
After watching this video lesson, you will understand how the trigonometric functions cotangent, secant, and cosecant are related to the sine, cosine, and tangent functions.
4. Trigonometric Ratios and Similarity
Where do terms like sine, cosine and tangent come from? In this lesson, we'll learn about how similarity with right triangles leads to trigonometric ratios.
5. Unit Circle: Memorizing the First Quadrant
Memorizing the unit circle can be a daunting task, but this lesson will show you a pattern to help you memorize the points, degree measures, and radian measures for the entire first quadrant.
6. Using Unit Circles to Relate Right Triangles to Sine & Cosine
The unit circle is a helpful tool for understanding trigonometric concepts. In this lesson, we'll look at right triangles on the unit circle to better grasp sine and cosine.
7. Special Right Triangles: Types and Properties
Not all right triangles are the same. In this lesson, we'll look at two special right triangles (30-60-90 and 45-45-90) that have unique properties to help you quickly and easily solve certain triangle problems.
8. Trigonometric Function Values of Special Angles
After watching this video lesson, you will better understand the six trigonometric functions. You will also know what special angles there are and what the trigonometric values for these special angles are.
9. Law of Sines: Definition and Application
Don't get stuck trying to find missing sides or angles in a triangle. Use the Law of Sines to rescue you from any perilous triangle in which you have just a few pieces of information.
10. Law of Cosines: Definition and Application
In this lesson, we'll learn how to solve problems involving three sides and one angle in a triangle. The Law of Cosines, a modification of the Pythagorean Theorem, will save the day.
11. The Double Angle Formula
When you encounter a doubled angle, there are special formulas that can help you handle trigonometric value. In this lesson, we'll define and practice using the double angle formulas for sine, cosine and tangent.
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Other chapters within the ORELA Mathematics: Practice & Study Guide course
- ORELA Math: Properties of Real Numbers
- ORELA Math: Fractions
- ORELA Math: Decimals & Percents
- ORELA Math: Ratios & Proportions
- ORELA Math: Units of Measure & Conversions
- ORELA Math: Logic
- ORELA Math: Reasoning
- ORELA Math: Vector Operations
- ORELA Math: Matrix Operations & Determinants
- ORELA Math: Exponents & Exponential Expressions
- ORELA Math: Algebraic Expressions
- ORELA Math: Linear Equations
- ORELA Math: Inequalities
- ORELA Math: Absolute Value
- ORELA Math: Quadratic Equations
- ORELA Math: Polynomials
- ORELA Math: Rational Expressions
- ORELA Math: Radical Expressions
- ORELA Math: Systems of Equations
- ORELA Math: Complex Numbers
- ORELA Math: Functions
- ORELA Math: Piecewise Functions
- ORELA Math: Exponential & Logarithmic Functions
- ORELA Math: Continuity of a Function
- ORELA Math: Limits
- ORELA Math: Rate of Change
- ORELA Math: Calculating Derivatives & Derivative Rules
- ORELA Math: Graphing Derivatives
- ORELA Math: Applications of Derivatives
- ORELA Math: Area Under the Curve & Integrals
- ORELA Math: Integration Techniques
- ORELA Math: Applications of Integration
- ORELA Math: Foundations of Geometry
- ORELA Math: Geometric Figures
- ORELA Math: Properties of Triangles
- ORELA Math: Triangle Theorems & Proofs
- ORELA Math: Parallel Lines & Polygons
- ORELA Math: Quadrilaterals
- ORELA Math: Circles & Arc of a Circle
- ORELA Math: Conic Sections
- ORELA Math: Geometric Solids
- ORELA Math: Analytical Geometry
- ORELA Math: Trigonometric Graphs
- ORELA Math: Solving Trigonometric Equations
- ORELA Math: Trigonometric Identities
- ORELA Math: Sequences & Series
- ORELA Math: Graph Theory
- ORELA Math: Set Theory
- ORELA Math: Statistics Overview
- ORELA Math: Summarizing Data
- ORELA Math: Tables, Plots & Graphs
- ORELA Math: Probability
- ORELA Math: Discrete Probability Distributions
- ORELA Math: Continuous Probability Distributions
- ORELA Math: Sampling
- ORELA Math: Regression & Correlation
- ORELA Mathematics Flashcards