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Cogito

Trigonometry · Chapter 3 · Lesson 3

Practice Worksheet

Graphing Tangent

A graph with holes in it.

12 problems · about 21 minutes · F-TF.B.5, F-IF.C.7

NameDate

Figure — use these to answer the problems

Follow the curve toward an asymptote and watch it climb without ever reaching the line.
-8-8-6-6-4-4-2-222446688
y = 1 tan(1x) + 0
a, vertical stretch1
b, cycles1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. What is the period of y = tan(2x), in degrees?

    Answer

  2. Why does the tangent graph have asymptotes?

    • Its denominator, cosine, is zero there.
    • The values simply get large.

  3. What is tan 0°?

    Answer

  4. What is tan 180°?

    Answer

  5. Period of y = tan(3x), in degrees?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. The first asymptote of y = tan x above 90°, in degrees?

    Answer

  2. What is tan 45°?

    Answer

  3. What is tan 135°?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Sort each property by whether it belongs to sine or to tangent.

    Write each item under the heading it belongs to: Has an amplitude · Period of 360° · Has vertical asymptotes · Period of 180°

    Sine

    Tangent

  2. How many asymptotes does y = tan x have between 0° and 360°?

    Answer

  3. The Period

    What is the period of y = tan x, in degrees?

    Answerdegrees

  4. The Break

    At which angle between 0° and 180° is tan x undefined?

    Answerdegrees