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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