How does cosine work

Therefore we use the Cosine Rule. Find the unknown side or angle in each of the following diagrams: a. Section 4: Sine And Cosine Rule Introduction This section will cover how to: Use the Sine Rule to find unknown sides and angles Use the Cosine Rule to find unknown sides and angles Combine trigonometry skills to solve problems Each topic is introduced with a theory section including examples and then some practice questions. At the end of the page there is an exercise where you can test your understanding of all the topics covered in this page.

You are allowed to use calculators in this topic. All answers should be given to 3 significant figures unless otherwise stated. Formulae You Should Know You should already know each of the following formulae: formulae for right-angled triangles formulae for all triangles NOTE: The only formula above which is in the A Level Maths formula book is the one highlighted in yellow.

You must learn these formulae, and then try to complete this page without referring to the table above. Sine Rule The Sine Rule can be used in any triangle not just right-angled triangles where a side and its opposite angle are known. Work out the answer to each question then click on the button marked. The triangle is not right-angled, and we don't know a side and its opposite angle, so we need to use the Cosine Rule.

The triangle is right-angled, and the question involves angles, so we need to use trigonometric ratios. The triangle is not right-angled, but we do know a side and its opposite angle, so we use the Sine Rule. The triangle is right-angled, but the question does not involve angles, so we need to use Pythagoras's Theorem.

Work out the answers to the questions below and fill in the boxes. Click on the. Incorrect Answers There were 0 questions where you used the See solution button.

There were 0 questions where the answer was left incorrect. There were 0 questions which you didn't attempt or check. It should come out to 0. If it doesn't - make sure the calculator is set to work in degrees and not radians. If we look at the general definition - we see that there are three variables: the measure of the angle x , and the lengths of the two sides Adjacent and Hypotenuse.

So if we have any two of them, we can find the third. In the figure above, click 'reset'. Imagine we didn't know the length of the hypotenuse H. From our calculator we find that cos60 is 0.

For every trigonometry function such as cos, there is an inverse function that works in reverse. These inverse functions have the same name but with 'arc' in front. What are the sin, cos, and tan buttons on my calculator for? And how do they work?

When might I ever actually want to calculate the sine or cosine something? Those, obviously, are all very important and very reasonable questions to ask. And they're also very important questions to answer. Which is precisely the task we will begin to undertake next time. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.

Jump to Navigation. What Are Sine, Cosine, and Tangent? November 18, We are currently experiencing playback issues on Safari. If you would like to listen to the audio, please use Google Chrome or Firefox.

The Quick And Dirty The ratios of the sides of a right triangle are completely determined by its angles. Because there are three sides of a triangle means that there are also three possible ratios of the lengths of a triangle's sides.

These three ratios are the sine, cosine, and tangent trigonometric functions. About the Author. Follow Facebook Linkedin. Subscribe Podcast Google Stitcher. You May Also Like The World of Trigonometry. The Math Dude. What is Trigonometry? What Is the Pythagorean Theorem? What Is Pascal's Triangle?