### Sine, Cosine, and Tangent

**Trigonometry** is the study of the relationships between the sides and angles of right triangles. The legs are called ** adjacent** or

**depending on which acute angle is being used.**

*opposite*

The three basic trigonometric ratios are called sine, cosine and tangent. For right triangle

**Sine Ratio:**

**Cosine Ratio:**

**Tangent Ratio:**

An easy way to remember ratios is to use SOH-CAH-TOA.

**A few important points:**

- Always
**reduce ratios**(fractions) when you can. - Use the Pythagorean Theorem to find the missing side (if there is one).
- If there is a radical in the denominator,
**rationalize the denominator.**

What if you were given a right triangle and told that its sides measure 3, 4, and 5 inches? How could you find the sine, cosine, and tangent of one of the triangle's non-right angles?

### Examples

#### Example 1

Find the sine, cosine and tangent ratios of

First, we need to use the Pythagorean Theorem to find the length of the hypotenuse.

#### Example 2

Find the sine, cosine, and tangent of

Find the length of the missing side.

#### Example 3

Find the sine, cosine and tangent of

This is a 30-60-90 triangle. The short leg is 6,

#### Example 4

Answer the questions about the following image. Reduce all fractions.

What is

### Review

Use the diagram to fill in the blanks below.

tanD=?? sinF=?? tanF=?? cosF=?? sinD=?? cosD=??

From questions 1-6, we can conclude the following. Fill in the blanks.

cos−−−−=sinF andsin−−−−=cosF .tanD andtanF are _________ of each other.

Find the sine, cosine and tangent of

### Review (Answers)

To see the Review answers, open this PDF file and look for section 8.7.