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Resources tagged with Trigonometric identities similar to Shape and Territory:

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Broad Topics > Trigonometry > Trigonometric identities

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Shape and Territory

Stage: 5 Challenge Level: Challenge Level:1

If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?

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Why Stop at Three by One

Stage: 5

Beautiful mathematics. Two 18 year old students gave eight different proofs of one result then generalised it from the 3 by 1 case to the n by 1 case and proved the general result.

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T for Tan

Stage: 5 Challenge Level: Challenge Level:1

Can you find a way to prove the trig identities using a diagram?

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Sine and Cosine for Connected Angles

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.

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Round and Round a Circle

Stage: 4 Challenge Level: Challenge Level:1

Can you explain what is happening and account for the values being displayed?

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Trig Reps

Stage: 5 Challenge Level: Challenge Level:1

Can you deduce the familiar properties of the sine and cosine functions starting from these three different mathematical representations?

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What Are Complex Numbers?

Stage: 5

This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and. . . .

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Polar Flower

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.

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Loch Ness

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Draw graphs of the sine and modulus functions and explain the humps.

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Reflect Again

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.

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Quaternions and Reflections

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

See how 4 dimensional quaternions involve vectors in 3-space and how the quaternion function F(v) = nvn gives a simple algebraic method of working with reflections in planes in 3-space.

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Quaternions and Rotations

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find out how the quaternion function G(v) = qvq^-1 gives a simple algebraic method for working with rotations in 3-space.

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An Introduction to Complex Numbers

Stage: 5

A short introduction to complex numbers written primarily for students aged 14 to 19.

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Octa-flower

Stage: 5 Challenge Level: Challenge Level:1

Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?