Math by Grades

Math by Topics

$Math Word Problems$

$Probability$

$Set Theory$

Math Worksheets $Math Worksheets$

Math for Specific Tests $SAT Math$
$ACT Math$
$GMAT Math$
$GRE Math$
$High School, Regents$

Math Fun and Games $Math Trivia$
$Math Games$

Exam Preparation

Math in Video Lessons $Basic Algebra$

$Engineering Math$
$Singapore Math$
Science

Others

$What's New$

Tangent Function

A series of free High School Trigonometry Video Lessons from Brightstorm.

Tangent Function
In right triangle trigonometry (for acute angles only), the tangent is defined as the ratio of the opposite side to the adjacent side. The unit circle definition is tan(theta)=y/x or tan(theta)=sin(theta)/cos(theta). The tangent function is negative whenever sine or cosine, but not both, are negative: the second and fourth quadrants. Tangent is also equal to the slope of the terminal side.

Evaluating the Tangent Function
When evaluating the tangent function, to find values of the tangent function at different angles, we first identify the reference angle formed by the terminal side and the x-axis. Then, we find the tangent of this reference angle and, based on which quadrant the terminal side is in, decide if tangent is positive or negative. Tangent is positive in the first and third quadrants, where both sine and cosine are positive and both are negative.

Graph of the Tangent Function
For a tangent function graph, create a table of values and plot them on the coordinate plane. Since tan(theta)=y/x, whenever x=0 the tangent function is undefined (dividing by zero is undefined). These points, at theta=pi/2, 3pi/2 and their integer multiples, are represented on a graph by vertical asymptotes, or values the function cannot equal. Because of unit circle symmetry over the y-axis, the period is pi/2.

Transforming the Tangent Graph
When graphing a tangent transformation, start by using a theta and tan(theta) t-table for -pi/2 to pi/2. In the case of y=Atan(Bx) or y=Atan(B(x-h)), define Bx or B(x-h) to be equal to theta and solve for x. Now use this equation to create a x and Atan(Bx) or Atan(B(x-h)) table, which will give coordinate pairs to plot.

Intercepts and Asymptotes of Tangent Functions
The tangent identity is tan(theta)=sin(theta)/cos(theta), which means that whenever sin(theta)=0, tan(theta)=0, and whenever cos(theta)=0, tan(theta) is undefined (dividing by zero). When the tangent function is zero, it crosses the x-axis. Therefore, to find the intercepts, find when sin(theta)=0. To find the vertical asymptotes determine when cos(theta)=0.

Custom Search

We welcome your feedback, comments and questions about this site - please submit your feedback via our Feedback page.

Useful Links:
Trigonometry

Custom Search

Amazon.com Widgets