Cogito
Trigonometry · Chapter 3 · Lesson 3
Graphing Tangent
A graph with holes in it.
12 problems · about 21 minutes · F-TF.B.5, F-IF.C.7
What this lesson teaches
The student graphs the tangent function and explains its asymptotes and period.
- Tangent is sine over cosine, so it breaks wherever cosine is zero.
- Its period is 180°, half that of sine.
- It has no amplitude, because it has no maximum or minimum.
Warm Up
Straightforward practice. Get the method working first.
5 problemsWhat is the period of y = tan(2x), in degrees?
Answer 90
Why 90°.
Why does the tangent graph have asymptotes?
Answer Its denominator, cosine, is zero there.
Why Cosine is zero there, so the division is undefined.
What is tan 0°?
Answer 0
Why sin 0° ÷ cos 0°.
What is tan 180°?
Answer 0
Why Sine is zero there.
Period of y = tan(3x), in degrees?
Answer 60
Why 180 ÷ 3.
Build It Up
The same ideas with more to keep track of.
3 problemsThe first asymptote of y = tan x above 90°, in degrees?
Answer 270
Why Add the period.
What is tan 45°?
Answer 1
Why Sine and cosine are equal there.
What is tan 135°?
Answer -1
Why Reference 45°, quadrant II, where tangent is negative.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each property by whether it belongs to sine or to tangent.
Answer Sine: Has an amplitude, Period of 360° · Tangent: Has vertical asymptotes, Period of 180°
Why Only a quotient can be undefined.
How many asymptotes does y = tan x have between 0° and 360°?
Answer 2
Why At 90° and 270°.
The Period: What is the period of y = tan x, in degrees?
Answer 180 degrees
Why 180°.
The Break: At which angle between 0° and 180° is tan x undefined?
Answer 90 degrees
Why 90°.