Cambridge Additional Mathematics

210 The unit circle and radian measure (Chapter 8)

Discovery 1 The trigonometric ratios

In this Discovery we explore the signs of the trigonometric ratios in each quadrant of the unit circle.

What to do:

1 Click on the icon to run the Unit Circle software.

Drag the point P slowly around the circle.

Note thesignof each trigonometric ratio in each quadrant.

Quadrant cosμ sinμ tanμ

1 positive

2

3

4

2 Hence note down the trigonometric ratios which are

positivein each quadrant.

From theDiscoveryyou should have found that:

² sinμ,cosμ, andtanμare positive in quadrant 1

² onlysinμis positive in quadrant 2

² onlytanμis positive in quadrant 3

² onlycosμis positive in quadrant 4.

We can use a letter to show which trigonometric ratios are

positive in each quadrant. The A stands forallof the ratios.

You might like to remember them using

All Silly Turtles Crawl.

Example 6 Self Tutor

Use a unit circle diagram to find the values of cos(¡ 270 ±) andsin(¡ 270 ±).

cos(¡ 270 ±)=0 fthex-coordinateg

sin(¡ 270 ±)=1 fthey-coordinateg

THE UNIT

CIRCLE

y

x

2 nd 1 st

3 rd 4 th

O

y

O x

S A

T C

y

x

2 nd 1 st

3 rd 4 th

O

y

x

(0 1),

-270° 90°

O

cyan magenta yellow black

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_08\210CamAdd_08.cdr Monday, 23 December 2013 1:56:33 PM BRIAN