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This section looks at Sin, Cos and Tan within the field of trigonometry.

A right-angled triangle is a triangle in which one of the angles is a right-angle. The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question and the right angle. The opposite side is opposite the angle in question.

In any right angled triangle, for any angle:

The sine of the angle = the length of the opposite side                                    the length of the hypotenuse

The cosine of the angle = the length of the adjacent side                                       the length of the hypotenuse

The tangent of the angle = the length of the opposite side                                      the length of the adjacent side

So in shorthand notation: sin = o/h   cos = a/h   tan = o/a Often remembered by: soh cah toa

Example

Find the length of side x in the diagram below:

The angle is 60 degrees. We are given the hypotenuse and need to find the adjacent side. This formula which connects these three is: cos(angle) = adjacent / hypotenuse therefore, cos60 = x / 13 therefore, x = 13 × cos60 = 6.5 therefore the length of side x is 6.5cm.

This video will explain how the formulas work.

The Graphs of Sin, Cos and Tan - (HIGHER TIER)

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