Everything Maths Grade 10

Step 2: Plot the points and join with a smooth curve

30 ◦ 60 ◦ 90 ◦ 120 ◦ 150 ◦ 180 ◦ 210 ◦ 220 ◦ 270 ◦ 300 ◦ 330 ◦ 360 ◦

 3

 2

 1

1

2

3



f()

There is an easy way to visualise the tangent graph. Consider our definitions ofsinandcosfor right-angled
triangles:

sin

cos

=

(

opposite

hypotenuse

)

(

adjacent

hypotenuse

)

=

opposite

hypotenuse



hypotenuse

adjacent

=

opposite

adjacent

=tan

So for any value of:tan=
sin
cos

So we know that for values offor whichsin= 0, we must also havetan= 0. Also ifcos= 0the value
oftanis undefined as we cannot divide by 0. The dashed vertical lines are at the values ofwheretanis
not defined and are called the asymptotes.

Asymptotes: the lines= 90°and= 270°

Period: 180 °
Domain:f: 0° 360 °; ̸= 90°; 270°gRange:ff() :f() 2 Rg

x-intercepts:(0°; 0),(180°; 0),(360°; 0)y-intercept:(0°; 0)

Functions of the formy=atan+q EMA5G

Investigation: The effects ofaandqon a tangent graph

On the same set of axes, plot the following graphs for 0 ° 360 °:

1.y 1 =tan 2

2.y 2 =tan 1

3.y 3 =tan

4.y 4 =tan+ 1

5.y 5 =tan+ 2

Use your results to deduce the effect ofq.

Chapter 6. Functions 197