Cambridge International AS and A Level Mathematics Pure Mathematics 1

P1^

7

Trigonometrical functions

Trigonometrical functions

The simplest definitions of the trigonometrical functions are given in terms of

the ratios of the sides of a right-angled triangle, for values of the angle θ between

0° and 90°.

In figure 7.4

sinθ= cosθ= t

opposite

hypotenuse

adjacent

hypotenuse

aanθ=.

opposite

adjacent

Sin is an abbreviation of sine, cos of cosine and tan of tangent. You will see from

the triangle in figure 7.4 that

sin θ = cos (90° − θ) and cos θ = sin (90° − θ).

Special cases

Certain angles occur frequently in mathematics and you will find it helpful to

know the value of their trigonometrical functions.

(i) The angles 30° and 60°

In figure 7.5, triangle ABC is an equilateral triangle with side 2 units, and AD is a

line of symmetry.

Using Pythagoras’ theorem

AD^2 + 12 = 22 ⇒ AD = 3.

opposite

adjacent

hypotenuse

90° – θ

θ

Figure 7.4

30°

60°

D

B C

A

2

1

Figure 7.5