Tangent Parent Graph Math

Y a tan b x c d.

Tangent parent graph math. Voiceover what i hope to do in this video is get some familiarity with the graph of tangent of theta. At π 2 radians 90 and at π 2 90 3 π 2 270 etc the function is officially undefined because it could be positive infinity or negative infinity. Those asymptotes give you some structure from which you can fill in the missing points. This confirms that tangent is an odd function since tan x tan x.

Below is a graph of y tan x showing 3 periods of tangent. The tangent function has a completely different shape. In this graph we can see that y tan x exhibits symmetry about the origin. The following table shows the transformation rules for functions.

The following figures show the graphs of parent functions. To plot the parent graph of a tangent function f x tan x where x represents the angle in radians you start out by finding the vertical asymptotes. This is because for multiples of displaystyle frac pi 2 we have to divide by 0 to get the tangent. So now that we have learned about the six standard parent functions of trigonometry we are ready to take a look at how we can manipulate the parent.

Linear quadratic cubic absolute reciprocal exponential logarithmic square root sine cosine tangent. Note also that there is a vertical asymptote every pi radians. The only differences you can see are the values of theta where the asymptotes and x intercepts occur. This creates the asymptote.

This is called the period of the graph. Note the tangent graph repeats itself cycles every pi radians the x. Reflecting the graph across the origin produces the same graph. It goes between negative and positive infinity crossing through 0 and at every π radians 180 as shown on this plot.

This graph repeats itself one half of a revolution of the unit circle. Scroll down the page for more examples and solutions. That is my x axis and the unit circle would look something like this. You can find the parent graph of the cotangent function f x cot x.

Let s say that s a y axis and this is my x axis. To plot the tangent and the cotangent graph we choose a set of points and form a table of values with which we plot the points on the x y coordinate axis to obtain the required graph. Tan θ sin θ cos θ 1 cos θ sin θ 1 cot θ. The parent graphs of tangent and cotangent are comparable because they both have asymptotes and x intercepts.

Find the vertical asymptotes so you can find the domain. And to do that i ll set up a little unit circle so that we can visualize what the tangent of various thetas are.