What are the Sine and Cosine Rule

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So far we have been working with right-angled triangles. We discovered that Pythagoras' Theorem and Trigonometry allow us to calculate lengths in right-angled triangles. Trigonometry we also use when we want to calculate angles in right-angled triangles. But what do we do when we are not given a right-angled triangle? How do we calculate lengths and angles in non-right-angled triangles? In those cases we use the Sine and Cosine rule (which are actually still based upon the trigonometric ratios in right-angled triangles). Have a proper look at all of the following videos and make sure you know exactly how to approach this important IGCSE maths topic. Good luck and have fun!

Sine rule

If you have to calculate lengths and angles in non-right-angled triangles, you first check whether you can apply the Sine rule. The following videos will show you step by step what you need to do and which questions you should ask yourself. Do yourself a favour and examine all videos in the correct order. Each video will include something new to consider which will prepare you to successfully answer the example questions at the end.

Solving more Example Questions about the Sine Rule

Once you know what the Sine Rule is and how we can use it to calculate lengths and angles in all triangles, it is time to study the following maths example questions during your maths revision. The first video will prove the sine rule to you and show you it is not a magic formula! The next three videos will provide you with example questions in which the sine rule is used to calculate lengths and angles. Make sure to study all videos for every time something new will be added (something to take care of, a tip etc). So pass your IGCSE GCSE Maths exam and look at the following maths activities!

Cosine rule

In some situations you will be unable to apply the sine rule. Make sure to know exactly when you can and cannot use the sine rule. Also be sure of the order of questions you ask yourself when analysing these types of questions. When you cannot apply the sine rule, your last resort is the Cosine rule. The cosine rule will allow you to calculate lengths and angles in non-right-angled triangles too! And do not worry - after the cosine rule there will be no more surprises/rules for trigonometry. If you truly want to understand the cosine rule and want to be able to apply it with confidence, then study all the videos below in the correct order. Good luck!

The previous three videos explain step by step to you how to use the Cosine Rule to calculate angles and lengths in triangles. Hopefully you have studies all three maths activities during your maths revision. Do not think you know it all now and study the next two example questions about the Cosine Rule. Once you have studied those too you will understand everything about the Cosine Rule and pass your next IGCSE GCSE Maths exam.

Activity

The worksheet below I created for you to practice your understanding of the sine and cosine rule. If you want to be successful and pass your next maths exam, analyse for each question the situation properly and decide which strategy (sine or cosine rule) to use. I hope you can read the numbers properly because for some reason the quality decreased after uploading the document. Scroll all the way down for the answers (not too quickly of course because you first want to try it yourself!). Good luck and have fun!!

Past Exam Question involving Cosine Rule and more

Check the next video during your maths revision. I will solve a past paper question which includes a question about the cosine rule. I will also explain how to use Trigonometry and Pythagoras' Theorem to calculate lengths and how to calculate the volume of prisms.

Past Paper Question about Bearings, Sine and Cosine rule

One of you asked me to help with the following maths question. I will solve this past paper question for you and explain how to use the sine rule, how to use the cosine rule and how to calculate bearings. A great activity to practise during your maths revision!

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