This is an exploratory activity designed to help students go beyond learning trigonometric ratios as rote learning of special ratios involving sides of triangles.
It attempts to make students aware of the invariance of the special ratios sine, cosine and tangent for specific values of angle size. The special ratios (of given angle size) do not change when angle is placed differently in right angled triangles of different sizes or positions.
However, the concept of the special ratios are defined.
(Refer to other online resources for reference)
The sine (sin) of an angle marked in a right angled triangle is the ratio of the length of the side opposite the angle divided by the length of the hypotenuse.
The cosine (cos) of an angle marked in a right angled triangle is the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse.
The tangent (tan) of an angle marked in a right angled triangle is the ratio of the length of the side opposite to the angle divided by the length of the side adjacent to the angle.
Weaker students may require the help of teachers to guide and explain the investigation process especially with regards to the invariance.
