A-level Physics (Advancing Physics)/Vectors/Trigonometry

Trigonometry is the study of the ratios between sides on a right-angled triangle. Consider the following diagram:



Depending on the value of the angle BAC, the ratios between the three sides of the triangle will vary. These three sides are generally given the names 'hypotenuse' (H), 'opposite' (O) and 'adjacent' (A). The opposite side is opposite the angle being considered. The hypotenuse is the side opposite the right angle, and the adjacent side is the remaining side, which is also next to the angle being considered.

The three basic trigonometric ratios, in relation to an acute angle θ, are the sine, cosine and tangent ratios, as follows:

$$\sin{\theta} = \frac{O}{H}$$

$$\cos{\theta} = \frac{A}{H}$$

$$\tan{\theta} = \frac{O}{A}$$

It is often helpful to remember them by using the mnemonic 'SOH-CAH-TOA'.

These ratios can be calculated using the appropriate buttons on a scientific calculator. In addition, if you already know the ratio between two sides, and wish to calculate the angle from it, you can use the sin−1, cos−1 and tan−1 buttons to use the inverse function. These functions are technically known as arcsin, arccosin and arctan.