How to Use Tan on the Graphing Calculator

The tangent button on a graphing calculator is invaluable for solving trigonometry problems.

Decades ago, students needed to painstakingly use a slide rule to find the answer to a trigonometric problem involving tangents. Now, a graphing calculator makes the process quick and easy.

Finding an Unknown Side

As a trigonometric function, tangent (Tan) represents the ratio between the side opposite an angle in a right triangle and the side next to the angle. Therefore, if you need to find the length of a side in a triangle, you would press the "Tan" button on the calculator, enter the angle measure, close the parentheses, and hit "Enter."

Finding an Unknown Angle

The reverse process is used to find an unknown angle. Divide the side opposite the angle by the adjacent side. Then use the second function of the tangent button (called the arctan or inverse tan) by pressing "2nd" and then "Tan." Enter the number that you got by dividing the sides, close the parentheses, and press "Enter."

Tangent Graph

The "Tan" button on the graphing calculator can also be used to graph a tangent function. For example, to graph 2tan(x) -3, you would press "y=" and then enter the function using the "Tan" button to represent the tangent in the equation. Pressing "Graph" will then display the function visually on the coordinate plane.

References

• Clark University: Right Triangles