Everything Maths Grade 10

Therefore:

sin 0 °=

opposite

hypotenuse

=

0

hypotenuse

= 0

cos 0 °=

adjacent

hypotenuse

=

hypotenuse

hypotenuse

= 1

tan 0 °=

opposite

adjacent

=

0

adjacent

= 0

When= 90°the length of the adjacent side is equal to 0 and the length of the opposite side is equal to the
length of the hypotenuse. Therefore:

sin 90 °=

opposite

hypotenuse

=

hypotenuse

hypotenuse

= 1

cos 90 °=

adjacent

hypotenuse

=

0

hypotenuse

= 0

tan 90 °=

opposite

adjacent

=

opposite

0

=undefined

Now we can extend our knowledge of special angles.
 0° 30° 45° 60° 90°
sin 0 1
2

1

p

2

p

3

2

1

cos 1

p

3

2

1

p

2

1

2

0

tan 0 1

p

3

1 p 3 undefined

Worked example 11: Ratios in the Cartesian plane

QUESTION

P(3; 4)is a point on the Cartesian plane with originO.is the angle betweenOPand the positivex-axis.

Without using a calculator, determine the value of:

1.cos

2. 3 tan
   3.^12 cosec

SOLUTION

Step 1: Sketch pointPin the Cartesian plane and label the angle

0

y

x

P(3;4)



134 5.8. Defining ratios in the Cartesian plane