# Ch 9: Trigonometric Ratios

### About This Chapter

## Trigonometric Ratios - Chapter Summary

In this informative chapter, our professional instructors present trigonometric ratios. Our lessons cover the sine and cosine functions in trigonometry, as well as the equations associated with circular functions. Other topics covered in this fun chapter include using compass bearings to solve real world problems and relating right triangles to cosine and sine using unit circles. You'll also review how to apply the difference and sum identities. This chapter is designed to help you:

- Use angles of elevation and depression to solve problems
- Find the area of a triangle using sine
- Understand the formula associated with half angle
- Explain the basic trigonometric identities

Our short video and text lessons cover all the important topics you need to know to get caught up in class or study for a test. If you have questions as you work through the chapter, you're welcome to reach out to one of our instructors. It's easy to go back or jump forward to a specific section of a video lesson using the video tabs feature. You can access these tools 24 hours a day on your mobile device or computer for fast, convenient studying.

### 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. Circular Functions: Equations & Examples

In this lesson, we will learn how to define the basic trigonometric functions using a circle. In doing so, every angle in a circle will be paired with an ordered (x,y) point in the coordinate plane using the basic trigonometric functions.

### 3. Solving Real World Problems With Compass Bearings

There are several methods to indicate which way an object is heading by using a compass. In this lesson, we will focus on three figure compass bearings to solve real world problems.

### 4. Problem-Solving with Angles of Elevation & Depression

In this lesson, you'll explore the difference between angles of elevation and depression. You'll also learn how to solve problems related to angles of elevation and depression using basic trigonometric relationships

### 5. 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.

### 6. Using Sine to Find the Area of a Triangle

Since you first started working with triangles in math class, chances are you've been exposed to the formula for the area of a triangle. However, that is only good if you know the height of the triangle. This lesson shows you how to get around that.

### 7. Applying the Sum & Difference Identities

Watch this video lesson to learn the six sum and difference identities for the trig functions of sine, cosine, and tangent. Also, learn how you can use them to your advantage when solving tough trig problems.

### 8. Half Angle: Rule, Formula & Examples

If we know at least the cosine of an angle, we can use formulas to find the sine, cosine and tangent of half that angle. These formulas are called half-angle formulas. In this lesson we state half-angle formulas, describe the rules for using them, and present examples.

### 9. List of the Basic Trig Identities

There are specific trig functions that have very special and very simple relationships with each other. Learn the main one and how you can use it to understand the others.

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### Other Chapters

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
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Integration
- Logarithmic & Exponential Functions
- Calculating Trigonometric 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