You will often encounter trigonometric functions in physics. You need to understand the basics of the sine, cosine and tangent, and their inverses: the arcsine, arccosine and arctangent.

The illustration above depicts an angle and three sides of a triangle. The sine (sin) of the angle θ (the Greek letter theta, pronounced “thay-tuh”) equals the ratio of the side opposite the angle divided by the triangle's hypotenuse. “Opposite” means the leg across from the angle, as the diagram reflects.

The cosine (cos) of θ equals the ratio of the side of the triangle adjacent to the angle, divided by the hypotenuse. “Adjacent” means the leg that forms one side of the angle.

Finally, the tangent (tan) of θ equals the ratio of the opposite side divided by the adjacent side.

These three ratios are constant for a given angle in a right triangle, no matter what the size of the triangle. They are useful because you are often given information such as the length of the hypotenuse and the size of an angle, and then asked to calculate one of the legs of the triangle. For instance, if asked to calculate the opposite leg, you would multiply the sine of the angle by the hypotenuse.

You may also be asked to use the arcsine, the arccosine or the arctangent. These are often written as sin⁻¹, cos⁻¹ and tan⁻¹. These are not the reciprocals of the sine, cosine and tangent! Rather, they supply the size of the angle when the value of the trigonometric function is known. For example, since sin 30° equals 0.5, the arcsine of 0.5 (or sin⁻¹ 0.5) equals 30°. This is also often written as arcsin(0.5); arccos and arctan are the abbreviations for arccosine and arctangent.

In the old days, scientists consulted tables for these trigonometric values. Today, calculators and spreadsheets can calculate them for you.