Everything Maths Grade 10

0

0 ◦

360 ◦

90 ◦

180 ◦

270 ◦

Quadrant II Quadrant I

Quadrant III Quadrant IV

A

all ratios

S

sin

T

tan

C

cos

This diagram is known as the CAST diagram.

We note the following using the general definitions of the trigonometric ratios:

• Quadrant I
  Both thexandyvalues are positive so all ratios are positive in this quadrant.


• Quadrant II
  Theyvalues are positive thereforesinand cosec are positive in this quadrant (recall thatsinand cosec
  are defined in terms ofyandr).


• Quadrant III
  Both thexand theyvalues are negative thereforetanandcotare positive in this quadrant (recall that
  tanandcotare defined in terms ofxandy).


• Quadrant IV
  Thexvalues are positive thereforecosandsecare positive in this quadrant (recall thatcosandsecare
  defined in terms ofxandr).

IMPORTANT!

The hypotenuse,r, is a length, and is therefore always positive.

VISIT:

The following video provides a summary of the trigonometric ratios in the Cartesian plane.

See video:2FSNatwww.everythingmaths.co.za

Special angles in the Cartesian plane

When working in the Cartesian plane we include two other special angles in right-angled triangles: 0° and
90°.

Notice that when= 0°the length of the opposite side is equal to 0 and the length of the adjacent side is
equal to the length of the hypotenuse.

Chapter 5. Trigonometry 133