problem

### Trig reps

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

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Trig reps

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

problem
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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.

problem
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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.

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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.

problem
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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?

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Polar Flower

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

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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.

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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?