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T1 Pythagoras’ theorem

Pythagoras’ Theorem shows the relationship between the sides of a right-angled triangle. Knowing the length of two sides of a right-angled triangle, the length of the third side can be calculated.

T2 Right triangle trigonometry

Sine, cos and tan can be defined using side lengths of a right-angled triangle. These side lengths are identified as either the hypotenuse or the opposite or adjacent sides to the angle.

T3 The sine rule

How can we apply trigonometry to triangles that do not possess a right-angle? The sine rule shows that the ratio of the length of a side, to the sine of its opposite angle, will be the same for all...

T4 Cosine rule

The cosine rule is a generalisation of Pythagoras’ theorem. If you have any two sides of a triangle, as long as you know the angle between them, you can calculate the length of the third side.

T5 Angular measurement and the unit circle

Angles are frequently measured in degrees. However, it is sometimes useful to define angles in terms of the length around the unit circle (a circle of radius = 1). This module introduces radians as a...

T7 Trigonometric equations

If you know the value of a trigonometric function, how do I find all the possible angles that satisfy this expression? The calculator may only give you one answer to an inverse trig question...


Trigonometry is a branch of mathematics involving the study of triangles. Ancient builders and mariners used it for finding lengths that are not physically measurable (because they were so large) but...