Trigonometry

Pythagoras' Theorem

Pythagoras' theorem. Pythagoras' theorem - the square on the hypotenuse is equal to the sum of the squares on the other two sides - is well known. In this tutorial we revise the theorem and use it to solve problems in right-angled triangles. A less familiar form of the theorem is also considered.

Trigonometric Ratios in a Right Angled Triangle

Trig ratios in a right angled triangle . Knowledge of the trigonometric ratios of sine, cosine and tangent is vital in very many fields of engineering, science and maths. This unit introduces them and provides examples of how they can be used to solve problems.

Trigonometric ratios of an Angle of Any Size

Trig ratios of an angle of any size. Knowledge of the trigonometric ratios sine, cosine and tangent is vital in many fields of engineering, maths and science. This unit explains how the sine, cosine and tangent of an arbitrarily sized angle can be found.

Radian Measurement

Radian measure . Most people usually learn to measure an angle in degrees. But in many scientific and engineering calculations radians are used in preference to degrees.

Solving Trigonometric Equations

Trigonometric equations. The strategy we adopt in solving trigonometric equations is to find one solution using knowledge of commonly occurring angles and then use the symmetries in the graphs of the trigonometric functions to deduce additional solutions.

Trigonometric Identities

Trigonometric identities. In this unit we consider trigonometric identities and how to use them to solve trigonometric equations.

Triangle Formulae

Triangle formulae. A common mathematical problem is to find the angles or lengths of the sides of a triangle when some, but not all, of these quantities are known. It is also useful to be able to calculate the area of a triangle from some of this information.

Trigonometric Functions

Cosec, sec and cot. In this unit we see how the three trigonometric ratios cosecant, secant and cotangent can appear in trigonometric identities and in the solution of trigonometric equations. Graphs of the functions are obtained from a knowledge of sine, cosine and tangent.

The Addition Formulae

The addition formulae. There are six so-called addition formulae often needed in the solution of trigonometric problems. In this unit we start with one and derive a second. Then we take another one as given and derive a second one from that. Finally we use these four to help us derive the final two.

The Double Angle Formulae

The double angle formulae. Double angle formulae are so called because they involve trigonometric functions of double angles e.g. sin 2A, cos 2A and tan 2A.

a cos x + b sin x = R cos(x - a)

a cos x + b sin x = R cos(x - a) . In this unit we explore how the sum of two trigonometric functions e.g. 3 cos x + 4 sin x, can be expressed as a single trigonometric function. Having the ability to do this enables us to solve trigonometric equations and find maximum and minimum values.