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. |
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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 23 September 'Starter of the Day' page by Judy, Chatsmore CHS: "This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles." 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." |
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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AnswersThere are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer. A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves. Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members. If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now: Subscribe |
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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/A-level exam paper questions (worked solutions are available for Transum subscribers).
More Trigonometry including visual aids, investigations and self-marking exercises.
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.
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 double-click the 'Check' button to make it float at the bottom of your screen.
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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