Let’s begin by restating the definition of the trigonometric ratios:

Definition:  If \(\theta \) is an acute angle in a right triangle, then

\(\large \sin \theta  = \Large \frac{{opposite  leg}}{{hypotenuse}}\)

\(\large \cos \theta  = \Large \frac{{adjacent  leg}}{{hypotenuse}}\)

\(\large \tan \theta  = \Large \frac{{opposite  leg}}{{adjacent  leg}}\)

The following diagram represents the right triangle along with their legs and hypotenuse.

Once we have the definition of sine, cosine, and tangent, finding those ratios is as easy as plugging in numbers.  Let’s try an example:

Example:  Find the value of \(\cos C\), we first remember the definition of cosine:

\(\cos C = \Large \frac{{adjacent  leg}}{{hypotenuse}}\)

Letting the figure from the definition be our guide, we see that the adjacent leg is \(12\) and the hypotenuse is \(20\). Then it’s as easy as plugging in the numbers.

\(\cos C = \Large \frac{{12}}{{20}} \approx 0.6000\), rounded to the nearest ten thousandth

So in this example, \(\cos C \approx 0.6000\).

Example:  Find the value of \(\cos A\) to the nearest ten thousandth.

Solution:  We use the same technique as in the previous example.  First we understand that the adjacent leg is \(20\), and the hypotenuse is \(29\). Then

\(\cos A = \Large \frac{{adjacent  leg}}{{hypotenuse}} = \Large \frac{{20}}{{29}} \approx 0.6897\), rounded to the nearest ten thousandth

So it is important when finding trigonometric ratios to remember to determine correctly which leg is the opposite, which is the adjacent, and which is the hypotenuse.  After that, it’s as easy as plug ‘n’ chug!

Below you can download some free math worksheets and practice.