Math Worksheets

Question: What is the period, asymptotes and x-intercepts of tan(3x)?

Can someone help me find the answers with some explanation. My math worksheet doesn’t explain it very well. How would I derive the answers from just the equation and then how would use all those information to start to graphing that equation?

Answer: tan (3x) has a period of 180°. That means that every 180°, the tan curve will be repeated. (Take at look at what a tan curve looks like. You will see that every time you add 180° on any degrees, you will get the same answer. Sorry, I couldn’t find any decent ones on the internet.)

To find asymptotes, let tan (3x) = tan (90°) [Every period of 90° on a tan curve, there is an asymptote.] Have you done general solutions yet? If so, apply them. (The general solution for tan a = tan b is a = 180°n + b, where n is an integer.)

tan (3x) = tan (90°)
3x = 180°n + 90°
x = 60°n + 30°

n = 0, x = 30°
n = 1, x = 90°
n = -1, x = -30°
n = 2, x = 150°
etc.

How many numbers you substitute into n will depend on your domain.

To find the x-intercepts of tan (3x), let tan (3x) = 0. Again, use general solutions.

tan (3x) = 0 = tan 0.
3x = 180°n + 0
x = 60°n
n = 0, x = 60°
n = 1, x = 180°
n = -1, x = -180°
etc.

Solving Multi-Step Equations with Variables on Both Sides