# Solving Problems in Trigonometry

## Using Trigonometric Identities to Solve Problems

## Video

This video from *patrickJMT* discusses properties of $\sin$, $\cos$ and $\tan$, and whether they are odd or even. This is a particularly useful property to remember when working on trigonometry problems.

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 an example of using double angle formulae for trigonometric functions to find particular angles. These formulae are also useful in integration problems.

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

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

This video from *Khan Academy* shows how to use identities for $\sin$ and $\cos$ which are derived from Pythagoras’ Theorem. These identities are very useful for simplifying expressions which can make solving problems much easier.

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

## Notes

These notes from MathCentre introduce some trigonometric identities that you may find useful. They also work through using these identities to solve trigonometric problems. There are also exercises with answers given which you can use to practice.

A pdf of this document can be downloaded here.

## Interactive Exercises

This NUMBAS exercise lets you test what you’ve learned and apply it to finding particular angles, or their associated trigonometric ratios.

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

## Pythagoras’ Theorem

## Video

This video from *patrickJMT* introduces Pythagoras’ theorem and gives a couple of worked examples of using it to solve for a side of a right-angled triangle, along with a word problem.

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 gives some examples of how to use Pythagoras’ theorem, for both right-angled triangles and for finding the diagonal of a cuboid. There are exercises throughout with answers at the end.

A pdf of this document can be downloaded here.

## Interactive Exercises

These NUMBAS exercises let you test what you’ve learned to find one side of a right angled triangle given the other two using Pythagoras’ theorem. The last part asks you to use Pythagoras’ Theorem to find the sine of an angle given its cosine, and vice versa.

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

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

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

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

## The Sine Rule

## Videos

This video from *Khan Academy* shows how to find the unknown sides and angles of a triangle given two angles and a side by using the Sine Rule.

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

## Notes

Page 1 of these notes from MathCentre introduces the sine rule, along with a worked example detailing how to use it. There are exercises at the end that you can use for practice.

A pdf of this document can be downloaded here.

## Interactive Exercises

These NUMBAS exercises allow you to use what you’ve learned to find the missing information for a triangle, given some information about its sides and angles.

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

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

## The Cosine Rule

## Videos

This video from *Khan Academy* shows how to solve for a side of a triangle using the cosine rule. It also gives instructions on how to compute the answer using a calculator.

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

## Notes

Page 2 of these notes from MathCentre introduces the cosine rule, along with a worked example detailing how to use it. There are exercises at the end that you can use for practice.

A pdf of this document can be downloaded here.

## Interactive Exercises

These NUMBAS exercises let you practise using the cosine rule to compute missing information for a triangle. There are two cases, one where you know all three sides, and one where you know two sides and an angle.

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

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

## Trigonometric Problems – Solving for Sides and Angles

## Videos

This video from *patrickJMT* shows how to find a side of a right-angled triangle using the trigonometric ratios.

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 introduce, and show how the sine, cosine and tangent trigonometric ratios are used in problem solving for right-angled triangles. There are exercises with answers included for practice.

A pdf of this document can be downloaded here.