Each of the four triangles above contains a right angle. The three sides are labelled a, b, and c in no particular order. One of the two angles that is not a right angle is labeled by the Greek letter a (read: alpha).

The three most commonly used trigonometric functions are the sine, the cosine, and the tangent. They are the trig functions that you will find on all scientific pocket calculators. They are sufficient for establishing the relations requested below.

Task. Fill in all empty slots in the table below. In each slot, you are asked to place an expression for one of the sides in one of the triangles (i) - (iv) in terms of one of the other sides and an appropriate trig function evaluated for a.

Example. In the first row of the table below, you are asked to place expressions for side a in terms of side b and angle a. The answers for triangles (i) and (ii) are shown.

Fill in all empty slots in the table similarly.

When done, compare your answers with those on Page 2.