Trigonometry: Tangent Identity

##The Tangent Identity

$$Tangent = \frac{sin(\theta)}{cos(\theta)}$$

In terms of a triangle, the tangent is the $\frac{opposite}{adjacent}$.

Tangent can be used just like other trig functions such as sine and cosine. Just like sine and cosine, tangent is a periodic function with an amplitude, midline, and period.

Tangent Identity

The next lesson in our series of trigonometric identities is the tangent identity! The tangent identity is something we have seen before!

We can find the tangent of a function by finding the ratio between the sine and the cosine.

$$\text{tan}(x) = \frac{\text{ sin }(x)}{\text{ cos }(x)}$$

Check your notes for the formula of cosine and sine!

Sum and Difference Identities of Tangent

To take this concept a step further, we will first look at the formula for the sum identity of tangent functions:

$$\tan(\alpha + \beta) = sin( \alpha + \beta) \cdot cos(\alpha + \beta)$$

We can also write this formula as:

$$\tan(\alpha + \beta) = \frac{\tan(\alpha) + \tan(\beta)}{1 - \tan(\alpha)\tan(\beta)}$$

Here is the formula for the difference identity of tangent functions:

$$\tan(\alpha - \beta) = \frac{\tan(\alpha) - \tan(\beta)}{1 + \tan(\alpha)\tan(\beta)}$$

In the next few lessons, you will learn about reciprocal identities, the pythagorean identity, and how to derive identities.

(Video) How to Use Tangent Sum and Difference Formulas

by Mario's Math Tutoring

In this video by Mario's Math Tutoring, you will learn how to use the tangent sum and difference identity formulas.