About This Chapter
Calculating Trigonometric Functions - Chapter Summary
In this chapter, our instructors explain the processes involved in calculating trigonometric functions. Lessons cover radians and degrees on the unit circle, examples of trigonometric functions and how to graph them. You'll also learn how to find the period of cosine and sine functions and the important concepts associated with graphing the tangent function. Once you complete these lessons, you should be able to:
- Use a formula to calculate small-angle approximation
- Calculate derivatives and integrals of trigonometric functions
- Solve integrals using trigonometric substitution
You can access the learning tools provided in this chapter on any mobile device or computer 24 hours a day. Each of our professionally designed video and text lessons is accompanied by a multiple-choice quiz that makes a great test preparatory exercise. If at any time you need help, feel free to reach out to one of our instructors.
1. Radians & Degrees on the Unit Circle
Angles are important in all kinds of fields, such as construction, science, math, navigation, and engineering. There are two units that we can use to measure angles: degrees and radians. In this lesson, learn how to use these units and how they are related to the unit circle.
2. Trigonometric Functions: Definition & Examples
In mathematics, trigonometric functions are functions of angles. This lesson will describe the 6 main trigonometric functions, use them to solve problems, and give some examples. The quiz at the end of the lesson will allow you to practice what you've learned.
3. How to Graph Trigonometric Functions
In this lesson, you'll learn how to read a trigonometric function so that you could recognize it on a graph. There isn't much math to it, you just have to know which numbers to look at.
4. How to Find the Period of Sine Functions
This lesson explains the forms that the sine function can take on and teaches us how to find the period of these functions. After learning how to find the period, we'll look at a real world application.
5. How to Find the Period of Cosine Functions
This lesson shows how to find the period of cosine functions. We then take it a step further and look at the amplitude, phase shift, and vertical shift of a cosine function and how to find all of these characteristics of cosine functions.
6. Graphing the Tangent Function: Amplitude, Period, Phase Shift & Vertical Shift
Take a look at how the graph of a tangent function and how we can transform it by making a few small changes to its equation. This video shows how to graph the original function and explains its transformations.
7. Small-Angle Approximation: Formula & Examples
There are approximations that you can use for the trigonometric functions when the angle is very small, which make the functions much easier to work with. In this lesson, learn all about the small angle approximations for sine, cosine, and tangent.
8. Calculating Derivatives of Trigonometric Functions
The trigonometric functions show up almost everywhere that you have a repeating pattern. In this lesson, learn how to find the derivatives of the trigonometric functions.
9. How to Calculate Integrals of Trigonometric Functions
Ever feel like you are going around in circles? Like, periodically you have your ups and downs? Well, sines and cosines go up and down regularly too. In this lesson, learn how to integrate these circular functions.
10. How to Use Trigonometric Substitution to Solve Integrals
In this lesson, we use each of the common integration techniques to solve different integrals. It's not always obvious which technique will be the easiest, so being familiar with an arsenal of methods might save you a lot of work!
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards