There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Trigonometry. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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### Trigonometry Starters:

Refreshing Revision: It is called Refreshing Revision because every time you refresh the page you get different revision questions.

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.

#### Which Side?

Arrange the diagrams in groups depending on whether the arrow is pointing to the opposite, adjacent or hypotenuse.

Transum.org/go/?to=whichside

### Curriculum for Trigonometry:

#### Years 7 to 9

Pupils should be taught to use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles more...

#### Years 10 and 11

Pupils 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 = kx 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 13

Pupils 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
sinθ ≈ θ,
cosθ ≈ 1 - ½θ2
tanθ ≈ θ,
Where θ is in radians more...

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
tanθ = sinθ ÷ cosθ
sin2θ + cos2θ = 1
sec2θ = 1 + tan2θ and
cosec2θ = 1 + cot2θ more...

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);
understand geometrical proofs of these formulae;
understand and use expressions for a cosθ + b sinθ in the equivalent forms of r cos (θ ± α) or r sin (θ ± α) more...

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 Baccalaureate

See the Geometry and Trigonometry sub-topics, syllabus statements, exam-style questions and learning resources for the IB AA course here.

### Exam-Style Questions:

There are almost a thousand exam-style questions unique to the Transum website.

### Feedback:

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 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 'starter-of-the-day' 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 on-line 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."

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To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."

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"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!!"

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"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."

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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"

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"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 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."

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"Very good starters, help pupils settle very well in maths classroom."

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"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 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."

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"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.
Thanks again"

Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast:

"My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please."

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"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."

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Comment recorded on the 9 April 'Starter of the Day' page by Jan, South Canterbury:

"Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you."

Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology:

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Comment recorded on the 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon:

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Comment recorded on the 23 September 'Starter of the Day' page by Judy, Chatsmore CHS:

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### 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 right-angled 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.

Having mastered right-angled triangle trigonometry pupils then progress to more advanced uses including the sine rule and cosine rules.

The use of a scientific or graphing calculator is essential for this topic and correct, efficient use of the calculator is an important skill to develop.

Here's a Trigonometry Wordsearch just for fun.

### 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 right-angled triangles.

Formulae to Remember: The traditional pairs or pelmanism game adapted to test recognition for formulae required to be memorised for GCSE exams.

Trig-Pythag Fusion: Problems requiring multi-step solutions using both Trigonometry and Pythagoras' Theorem

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 self-marking exercise on finding the exact values of sine, cosine and tangent of special angles.

Trigonometry Advanced: A self-marking exercise on the sine rule, cosine rule and the sine formula for finding the area of a triangle.

Common Trig Ratios Radians: A self-marking 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 ever-growing collection of Exam-Style 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:

Transum's Trigonometry Video

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 right-angled 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, self-marking exercise.

Three Dimensional Trigonometry Video: When you have mastered trigonometry in two dimensions it is time to practise solving three-dimensional problems.

Formulae for GCSE: These are the formulae candidates need to know for the GCSE(9-1) Maths exams.

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##### Suggested

A self-marking exercise on finding the exact values of sine, cosine and tangent of special angles given in radians.

### Teaching Notes:

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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 exam-style questions on the Angles of Elevation and Depression page.]"

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