If Then TrigonometryFinding the exact values of sine, cosine and tangent of angles if given a different trig ratio. 
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.
InstructionsTry 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. 



Transum.orgThis web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available. Please contact me if you have any suggestions or questions. 
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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? Comment recorded on the 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School: "Really good site. Lots of good ideas for starters. Use it most of the time in KS3." Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk: "Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!" 
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Go MathsLearning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Maths MapAre you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.  
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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/Alevel exam paper questions (worked solutions are available for Transum subscribers).
More Trigonometry including visual aids, investigations and selfmarking exercises.
The questions in this exercise are designed to be solved by drawing a diagram of a rightangled 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 righangled triangle containing the angle \( \theta \), opposite 8 and adjacent 15.
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 \( \frac{8}{17} \).
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 doubleclick the 'Check' button to make it float at the bottom of your screen.
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