YOU ARE LEARNING:

# The Tangent Graph

### The Tangent Graph

The Tangent graph is another ratio which we find in right-angled triangle trigonometry. We can display its shape on a graph.

Like the Sine and Cosine functions, we can plot the Tangent function on a graph. It refers to the ratio between the length of the **opposite** and **adjacent** sides in a right-angled triangle.

The Tangent function is defined as:

$tan(x) = \dfrac{opposite}{adjacent}$

For $y = tanx$ between 0 and 360, the graph meets the x axis at $0$ and what other value?

Similar to Sine and Cosine, we can find the angles which correlate to particular values of tan using the $tan^{-1}$ function. For example, the angle when $tanx=1$ is:

$tan^{-1}(1)=45\degree$

What is $tan^{-1}(0.5)$? Give your answer to 3 significant figures.

For $y = tanx$ between 0 and 360, $tan60 = \sqrt3$. Another value of x that would give $\sqrt3$ is: