Trigonometry involves the ratios of sides in right triangles. For a given angle in a right triangle, there is a leg opposite it, a leg adjacent to it, and the hypotenuse (the longest side). Look at the diagram at left, and take note of the legs that are adjacent and opposite to the angle at vertex A. Be sure to understand that the leg adjacent to angle A is the leg that is opposite angle B. The leg that is opposite angle A is the leg adjacent to angle B. The hypotenuse is always just the hypotenuse, regardless of what angle we are talking about.
The first trig ratio is sine, abbreviated sin. The sine of an angle is defined as the opposite leg over the hypotenuse. For example, the sine of angle A is 3/5. Remember that a fraction is really a division problem, so we can also compute 3 divided by 5, and say that the sine is 0.6.
The next trig ratio is cosine, abbreviated cos. The cosine of an angle is defined as the adjacent leg over the hypotenuse. For example, the cosine of angle A is 4/5, or 0.8.
The last basic trig ratio discussed in this article is tangent, abbreviated tan. The tangent of an angle is defined as the opposite leg over the adjacent leg. For example, the tangent of angle A is 3/4, or 0.75.
We can use the acronym SOH-CAH-TOA to help us remember these ratios. Sine is opposite over hypotenuse. Cosine is adjacent over hypotenuse. Tangent is opposite over adjacent. Many students write this acronym at the top of their exams before they begin, so that they won't forget it.
For practice, try computing the sine, cosine, and tangent of angle B in the above diagram. We use these trig ratios to help us solve problems involving missing angles or sides in a right triangle. For example, if we know that an angle has a sine of 0.6, we can use a trig chart or a scientific calculator to determine the actual degree measure of that angle. Conversely, if we know the degree measure of an angle, along with one of the involved sides, we can use one of the trig ratios along with a chart or calculator to determine the length of the missing side.
This article is just a very basic introduction to trig ratios. Students should certainly remember the SOH-CAH-TOA acronym and how it is used. Many test questions can be answered with just that alone.