Sine, cosine, tangent

What is an AC voltage? How much power does an AC power source supply?

Can you find the sum of the squared sine values?

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?

How can you represent the curvature of a cylinder on a flat piece of paper?

Prove that the shaded area of the semicircle is equal to the area of the inner circle.

Trigonometry, circles and triangles combine in this short challenge.

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees before being reflected across to the opposite wall and so on until it hits the screen.