# Introduction to Trigonometry

### Degrees and Radians

### Video

This video from *Khan Academy* explains the idea behind the radian, and why it is a natural unit for measuring angles.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

This video from *patrickJMT* shows how to convert a degree measurement for an angle to radians.

Note: All *patrickJMT* content is available for free at www.youtube.com/user/patrickJMT.

Patrick JMT’s Website: www.patrickjmt.com.

This video from *patrickJMT* shows how to convert a radian measurement for an angle to degrees.

Note: All *patrickJMT* content is available for free at www.youtube.com/user/patrickJMT.

Patrick JMT’s Website: www.patrickjmt.com.

### Notes

These notes from MathCentre explain the idea behind radians and show how to convert between radians and degrees. There are exercises with answers included so you can practise working with them.

A pdf of this document can be downloaded here.

### Interactive Exercises

This NUMBAS exercise lets you practise converting angle measurements from degrees to radians.

Please click here to view this NUMBAS question in another window.

This NUMBAS exercise lets you practice converting angle measurements from radians to degrees.

Please click here to view this NUMBAS question in another window.

### The Trigonometric Ratios: $\sin$, $\cos$ and $\tan$

### Video

This video from *Khan Academy* introduces the geometry of the right-angled triangle, briefly discusses Pythagoras’ Theorem and defines the standard trigonometric ratios of $\sin$, $\cos$ and $\tan$.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

### Notes

These notes from MathCentre define the trigonometric ratios for a right-angled triangle, along with some of their common values. Using a calculator to compute these ratios and their inverses is also discussed.

A pdf of this document can be downloaded here.

### Interactive Exercises

Use this NUMBAS exercise to practise computing trigonometric ratios for a right-angled triangle. If you try the question several times, you will get questions involving $\sin$, $\cos$ and $\tan$.

Please click here to view this NUMBAS question in another window.

### The Unit Circle

### Videos

This video from *Khan Academy* introduces the unit circle and the conventions for measuring angles. It then relates the geometry of the unit circle to the trigonometric ratios.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

This video from *patrickJMT* shows how to determine which quadrant of the unit circle a given angle corresponds to.

Note: All *patrickJMT* content is available for free at www.youtube.com/user/patrickJMT.

Patrick JMT’s Website: www.patrickjmt.com.

### Interactive Exercises

This NUMBAS exercise lets you practise your knowledge of the definition of the unit circle by determining the coordinates of a point on the circle given an angle in degrees.

Please click here to view this NUMBAS question in another window.

### Common Trigonometric Values

### Videos

This video from *patrickJMT* discusses the values of certain special angles and their associated trigonometric ratios, and does so in the context of the unit circle.

Note: All *patrickJMT* content is available for free at www.youtube.com/user/patrickJMT.

Patrick JMT’s Website: www.patrickjmt.com.

### Notes

These notes from MathCentre go through some problems involving some special angles in trigonometry and the values of their associated trigonometric ratios, which appear frequently in the subject.

A pdf of this document can be downloaded here.

### Interactive Exercises

This NUMBAS exercise allows you to familiarise yourself with these particular angles and values of the trigonometric ratios which you will encounter frequently.

Please click here to view this NUMBAS question in another window.

### Reciprocal Trigonometric Ratios: $\sec$, $\csc$ and $\cot$

### Videos

This video from *Khan Academy* shows how to compute the reciprocal trigonometric ratios $\sec$, $\csc$ and $\cot$ for a right-angled triangle (along with the standard ratios of $\sin$, $\cos$ and $\tan$).

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

### Notes

These notes from MathCentre introduce the reciprocal trigonometric ratios $\sec$, $\csc$ and $\cot$. Their definitions are covered and their graphs are depicted, and some problems are worked through. There are exercises with answers included which you can use for practice.

A pdf of this document can be downloaded here.

### Interactive Exercises

This NUMBAS exercise lets you practise working with the reciprocal trigonometric ratios $\sec$, $\csc$ and $\cot$ by finding values of these ratios for the special angles discussed in the Common Trigonometric Values subsection.

Please click here to view this NUMBAS question in another window.