### Cosines Rule

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

### Squ-areas

Three squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more triangular areas are enclosed. What is the area of this convex hexagon?

### Far Horizon

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

# Sine and Cosine

##### Stage: 4 Challenge Level:

The Flash "movie" allows students to see the flow of function values as the dot circles the centre point or origin. Students can be encouraged to see the "spot" values provided by a calculator as snap-shots of this flow.

Check that students grasp that an angle of zero is when the dot is at (1,0), that the red line corresponds to the Sine value and the blue line to the Cosine value.

There may be a need to guide students into noticing that there is a the change of sign, and noticing when it occurs.