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If Then Trigonometry

Finding the exact values of sine, cosine and tangent of angles if given a different trig ratio.

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Solve these "If Then" questions without using a calculator but giving exact answers in their simplest form. Use the / symbol to show a fraction and the root button to insert the square root sign if required.

If \( \sin \theta = \frac{3}{5} \)
then find \( \cos \theta \)

Correct Wrong

If \( \cos \theta = \frac{12}{13} \)
then find \( \tan \theta \)

Correct Wrong

If \( \tan \theta = \frac{3}{4} \)
then find \( \sin \theta \)

Correct Wrong

If \( 5\sin \theta = 4 \)
then find \( \tan \theta \)

Correct Wrong

If \( 13\cos \theta = 5 \)
then find \( \sin \theta \)

Correct Wrong

If \( 3\tan \theta = 4 \)
then find \( \cos \theta \)

Correct Wrong

If \( \tan \theta = 1 \)
then find \( \sin \theta \)

Correct Wrong

If \( 2\sin \theta = \sqrt{3} \)
then find \( \cos \theta \)

Correct Wrong

If \( 2\cos \theta = 1 \)
then find \( \tan \theta \)

Correct Wrong

Check

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

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"I would like to thank you for the excellent resources which I used every day. My students would often turn up early to tackle the starter of the day as there were stamps for the first 5 finishers. We also had a lot of fun with the fun maths. All in all your resources provoked discussion and the students had a lot of fun."

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

Whose Idea Was This?

Did you enjoy doing this 'If Then Trigonometry' activity? Are you curious about who originally came up with this idea in Maths? Discover more about one of the mathematicians who is associated with this concept.

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Imagine you are on a desert island with nothing but a pack of playing cards. Do you have to stop learning mathematics? Of course not! Here are some great ideas for teachers, parents and tutors.

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Description of Levels

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Surds - Make sure you understand what surds are before starting the levels below.

Common Trig Ratios Level 1 - Find exact trig values for special angles up to and including ninety degrees

Common Trig Ratios Level 2 - Find the indicated lengths by solving trigonometric questions with exact solutions

Common Trig Ratios Level 3 - Mixed questions on exact trig values of special angles up to and including ninety degrees

Common Trig Ratios Level 4 - Find exact trig values for angles between ninety and three hundred and sixty degrees

Common Trig Ratios Level 5 - Solving trigonometric equations with given domains

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Trigonometry including visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Help

The questions in this exercise are designed to be solved by drawing a diagram of a right-angled triangle, choosing the lenghts of two of the sides using the given ratio then use Pythagoras' theorem to figure out the length of the third side. The required trig ratio can then be found from the diagram.

For example, if \(\tan \theta = \frac{8}{15} \) then find \( \sin \theta \)

Firstly sketch a righ-angled triangle containing the angle \( \theta \), opposite 8 and adjacent 15.

Example

The length of the hypotenuse can be calculated using pythagoras' Theorem to be \( \sqrt{8^2 + 15^2} = 17\).

Finally \( \sin \theta \) can be calculated as the opposite over the hypotenuse which is \( \frac{8}{17} \).

Common Trigonometric Ratios Video

Helpful Diagrams

Common Trig Ratios

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

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