# Trigonometric Functions

by M. Bourne

## Why learn about trigonometric functions...?

**Example problem:**

How high above sea level is the top of the Sydney Opera House? See how to do this in The Right Triangle and its Applications.

The** trig functions** are very important in technical subjects like science, engineering, architecture, and even medicine. You will come across them all the time so it's worth learning them well!

**Surveying** is one of the many applications. Road makers, bridge builders and those whose job it is to get buildings in the right place all use trigonometry in their daily work.

For more applications and examples of trigonometry in Interactive Mathematics, check out the many Uses of Trigonometry. See also: Math Tips - Trigonometry.

In this chapter we start by explaining the basic trigonometric functions using degrees (°), and in the later part of the chapter we will learn about radians and how they are used in trigonometry.

### Related Sections in "Interactive Mathematics"

Graphs of Trigonometric Functions, which are really helpful for understanding what is going on in trigonometry.

Analytic Trigonometry, which includes double angle formulas, trig ratios of the sum of 2 angles, trigonometric equations and inverse trig equations.

Polar Coordinates, which work in much the same way as the topics in this chapter.

Derivatives of the Transcendental Functions, which shows how to differentiate sin, cos, tan, csc, sec and cot functions.

Integration using Trigonometric Forms, where we see how our knowledge of trigonometry can make calculus easier.

Line Spectrum in Fourier Series, which is an advanced application of trigonometry.

And of course, don't miss the Uses of Trigonometry summary.

## In this Chapter

1. Angles - the building blocks of trigonometry. In **degrees**.

2. Sine, Cosine, Tangent & Reciprocals - these fractions are the key for all future trigonometry study.

3. Values of Trigonometric Functions - Why does sin 30° = 0.5?

4. The Right Triangle and Applications - includes **angle of depressio**n and **angle of elevation**.

5. Signs of the Trigonometric Functions - this is no big deal if you remember how we define the basic ratios. Includes an **interactive **document for seeing how the ratios of angles larger than 90 degrees work.

6. Trigonometric Functions of Any Angle - don't give up in this section!

7. Radians - the alternative to degrees - and much more useful.

8. Applications of Radian Measure - includes **arc length, area of a sector**, **angular velocity**, a **game** and pulleys.

9. Radians and the Trigonometric Ratios - how trigonometry works when the angle measure is **radians**.

This chapter starts with some reminders about Angles.