### Finding sine, cosine, tangent

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. 7167 x

Find the value of each trigonometric ratio to the nearest ten-thousandth.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question: Watch bellow how to solve this example: 3729 x

Find the value of each trigonometric ratio to the nearest ten-thousandth.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question: Watch bellow how to solve this example: 3160 x

Find the value of each trigonometric ratio.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question: Watch bellow how to solve this example:

### Geometry

Circles
Congruent Triangles
Constructions
Parallel Lines and the Coordinate Plane
Properties of Triangles

### Algebra and Pre-Algebra

Beginning Algebra
Beginning Trigonometry
Equations
Exponents
Factoring
Linear Equations and Inequalities
Percents
Polynomials