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

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 22.50 without using a calculator.

What Question?: Write down all the possible questions that could have been asked if this was the diagram provided in a mathematics textbook.

#### 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...

### Feedback:

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."

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"Dear Transum,

I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out 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."

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"I am an NQT and have only just discovered this website. I nearly wet my pants with joy.
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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Keep it up and 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 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 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

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"My year five children look forward to their daily challenge and enjoy the problems as much as I do. A great resource - thanks a million."

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.
Could we have some on angles too please?"

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"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

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"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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Thanks again"

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Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, :

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Best wishes from Inger Kisby"

### 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.

### Trigonometry Activities:

Common Trig Ratios: A self-marking exercise on finding the exact values of sine, cosine and tangent of special angles.

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

Trigonometry: 20 trigonometry questions in an online, self marking exercise.

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

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

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:

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

Trigonometry and Pythagoras: A trigonometry and Pythagoras theorem revision song

Trigonometry in 3D: This video from Corbettmaths goes through a typical 3D trigonometry question - finding an angle in a cuboid.

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:

### Search

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### Other

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#### Common Trig Ratios

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

Transum.org/go/?to=commontrigratios

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