Trigonometry Starters:Refreshing Revision: It is called Refreshing Revision because every time you refresh the page you get different revision questions.
Small images of these Starters :: Index of Starters Trigonometry Advanced Starters:Angle Thinking: Find the range of possible angles, x, for which tan x > cos x > sin x Cos 10 Equals p: Find the trigonometric values in terms of the given value, p. Exponential Trigonometry: Find, in degrees, all eight of the solutions to the given exponential, trigonometric equation Find The Radius: Find the radius of the circle from the small amount of information provided. Tan 22.5: Find an exact value for tan 22.5° without using a calculator. Tansum: Find the sum of the tangents of angles on a straight line. Trig Blot: Find all the measurements of the given triangle.
Curriculum for Trigonometry:Years 7 to 9Pupils should be taught to use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving rightangled triangles more... Years 10 and 11Pupils should be taught to compare lengths, areas and volumes using ratio notation and/or scale factors; make links to similarity (including trigonometric ratios) more... Pupils should be taught to recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = with x not equal to 0, {the exponential function y = k^{x} for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size} more... Pupils should be taught to know the exact values of the sine and cosine of 30, 45, 60 and 90 degrees; know the exact value of the tangent of 30, 45, and 60 degrees more... Pupils should be taught to {know and apply the sine and cosine rules to find unknown lengths and angles} more... Pupils should be taught to {know and apply Area = ½ ab sin C to calculate the area, sides or angles of any triangle} more... Years 12 and 13Pupils should be taught to understand and use the definitions of sine, cosine and tangent for all arguments; the sine and cosine rules; the area of a triangle in the form ½absin(C); Work with radian measure, including use for arc length and area of sector more... Pupils should be taught to understand and use the standard small angle approximations of sine, cosine and tangent Pupils should be taught to understand and use the sine, cosine and tangent functions; their graphs, symmetries and periodicity. Know and use exact values of sin, cos and tan for the following angles (in degrees and radians) 0°, 30°, 45°, 60°, 90°, 180° and multiples thereof more... Pupils should be taught to understand and use the definitions of secant, cosecant and cotangent and of arcsin, arccos and arctan; their relationships to sine, cosine and tangent; understanding of their graphs; their ranges and domains more... Pupils should be taught to understand and use Pupils should be taught to understand and use double angle formulae; use of formulae for sin (A ± B), cos (A ± B), and tan (A ± B); Pupils should be taught to solve simple trigonometric equations in a given interval, including quadratic equations in sin, cos and tan and equations involving multiples of the unknown angle more... Pupils should be taught to construct proofs involving trigonometric functions and identities more... Pupils should be taught to use trigonometric functions to solve problems in context, including problems involving vectors, kinematics and forces more... International BaccalaureateSee the Geometry and Trigonometry subtopics, syllabus statements, examstyle questions and learning resources for the IB AA course here. ExamStyle Questions:There are almost a thousand examstyle questions unique to the Transum website. Feedback:Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College: "Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work" Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School: "What a brilliant website. We have just started to use the 'starteroftheday' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources online we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and 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! Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield: "I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information." Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je: "I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson." Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay: "An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!" Comment recorded on the 6 May 'Starter of the Day' page by Natalie, London: "I am thankful for providing such wonderful starters. They are of immence help and the students enjoy them very much. These starters have saved my time and have made my lessons enjoyable." Comment recorded on the 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull: "Dear Transum, Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology: "This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative." Comment recorded on the 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai: "It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages." Comment recorded on the s /Indice 'Starter of the Day' page by Busolla, Australia: "Thank you very much for providing these resources for free for teachers and students. It has been engaging for the students  all trying to reach their highest level and competing with their peers while also learning. Thank you very much!" Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne: "Very good starters, help pupils settle very well in maths classroom." Comment recorded on the 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy: "3 NQTs in the department, I'm new subject leader in this new academy  Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!" Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School: "My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions." 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!" Comment recorded on the 9 May 'Starter of the Day' page by Liz, Kuwait: "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 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK: "I am an NQT and have only just discovered this website. I nearly wet my pants with joy. Comment recorded on the 2 May 'Starter of the Day' page by Angela Lowry, : "I think these are great! So useful and handy, the children love them. Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry: "Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils. Comment recorded on the 14 October 'Starter of the Day' page by Inger Kisby, Herts and Essex High School: "Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work." Comment recorded on the 2 April 'Starter of the Day' page by Mrs Wilshaw, Dunsten Collage,Essex: "This website was brilliant. My class and I really enjoy doing the activites." 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 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales: "A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access Starters for the whole month so I can use favourites with classes I see at different times of the week. Thanks." Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School: "We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory." Comment recorded on the s /Coordinate 'Starter of the Day' page by Greg, Wales: "Excellent resource, I use it all of the time! The only problem is that there is too much good stuff here!!" Comment recorded on the 7 December 'Starter of the Day' page by Cathryn Aldridge, Pells Primary: "I use Starter of the Day as a registration and warmup activity for my Year 6 class. The range of questioning provided is excellent as are some of the images. Comment recorded on the 16 March 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy: "I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson." Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset: "A set of real life savers!! Comment recorded on the 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon: "Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated." Comment recorded on the 3 October 'Starter of the Day' page by Fiona Bray, Cams Hill School: "This is an excellent website. We all often use the starters as the pupils come in the door and get settled as we take the register." 
Notes:Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Pupils begin by learning the names on the sides of a rightangled triangle relative to the angles. They then learn the ratios of the lengths of these sides and the connection these ratios have with the size of the angles.
Trigonometry Teacher Resources:3D Trigonometry Presentation: A slide presentation (a poem) introducing using trigonometry (including Pythagoras' Theorem) to find lengths and angles on three dimensional shapes. Inverse Trig Calculator: This calculator is designed to find all of the angles for a given trigonometric ratio and show them on a graph. Triangle Solver: Provide and three measurements for a triangle and this application will work out the remaining sides, angles and area. Trig Tour: See angles, in either degrees or radians, on the unit circle and the graph of the trigonometric function. Trigonometry Activities:Which Side?: Arrange the diagrams in groups depending on whether the arrow is pointing to the opposite, adjacent or hypotenuse. Trigonometry: Sine, cosine and tangent ratios are used to find sides and angles in rightangled triangles. Formulae to Remember: The traditional pairs or pelmanism game adapted to test recognition for formulae required to be memorised for GCSE exams. Trigonometry in 3D: Calculate the lengths of sides and the size of angles in three dimensional shapes. If Then Trigonometry: Finding the exact values of sine, cosine and tangent of angles if given a different trig ratio. Common Trig Ratios Degrees: A selfmarking exercise on finding the exact values of sine, cosine and tangent of special angles. Trigonometry Advanced: A selfmarking exercise on the sine rule, cosine rule and the sine formula for finding the area of a triangle. Common Trig Ratios Radians: A selfmarking exercise on finding the exact values of sine, cosine and tangent of special angles given in radians. Alternatively, for the more advanced student, there is an evergrowing collection of ExamStyle Questions with worked solutions on the topic of Trigonometry. Trigonometry Investigations:Search for Infinity: Manipulate the Lissajou curve to produce a perfectly symmetrical (vertically and horizontally) infinity symbol. Trigonometry Videos:Trigonometry Video: The basic trigonometric ratios are sine, cosine and tangent and are used to find the lengths of sides and the size of angles in rightangled triangles. Trigonometry and Pythagoras: A trigonometry and Pythagoras theorem revision song Common Trig Ratios Video: You may not realise that it is possible to find sin60° or tan45° without a calculator. This video is to help you do the online, selfmarking exercise. Three Dimensional Trigonometry Video: When you have mastered trigonometry in two dimensions it is time to practise solving threedimensional problems. Formulae for GCSE: These are the formulae candidates need to know for the GCSE(91) Maths exams. Trigonometry External Links:Links to other websites containing resources for Trigonometry are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below: SearchThe activity you are looking for may have been classified in a different way from the way you were expecting. You can search the whole of Transum Maths by using the box below.
OtherIs there anything you would have a regular use for that we don't feature here? Please let us know.

Teaching Notes:Many Transum activities have notes for teachers suggesting teaching methods and highlighting common misconceptions. There are also solutions to puzzles, exercises and activities available on the web pages when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page. A Transum subscription also gives you access to the 'Class Admin' student management system, downloadable worksheets, many more teaching resources and opens up adfree access to the Transum website for you and your pupils.  
CommentsHave today's Starter of the Day as your default homepage. Copy the URL below then select Set as your homepage (if you are using Internet Explorer)
Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments. 
John Rodger,
Thursday, November 17, 2022
"Hi, I have looked for something that specifically looks at angles of elevation and depression. Unable to find these as a separate of questions. Do you have a specific of questions relating to this?
Many thanks.
[Transum: Thanks for your comment John. You can find examstyle questions on the Angles of Elevation and Depression page.]"