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There are **13** NRICH Mathematical resources connected to **Trigonometric identities**, you may find related items under Pythagoras and trigonometry.

Problem
Primary curriculum
Secondary curriculum
### T for Tan

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Loch Ness

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Octa-flower

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shape and Territory

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Trig Reps

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

Age 16 to 18

Challenge Level

Interactive
Primary curriculum
Secondary curriculum
### Round and Round a Circle

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quaternions and Reflections

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quaternions and Rotations

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sine and Cosine for Connected Angles

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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polar Flower

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

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### What Are Complex Numbers?

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 their derivatives and proves that e^(i pi)= -1.

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Reflect Again

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.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Why Stop at Three by One

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.

Age 16 to 18