Page 11 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes

1. Find the most general value of satisfying :

(i) (ii)

(iii) (iv)

2. Find the most general value of satisfying :

(i) (ii)

(iii) (iv)

3. Find the most general value of satisfying :
(i) tan = –1 (ii)

(iii) cot = –1

1.2 Trigonometric Function

The trigonometric ratios – sine, cosine, and tangent – are based on properties of right triangles.
The function values depend on the measure of the angle. The functions are outlined below.
sine x = (side opposite x)/hypotenuse
cosine x = (side adjacent x)/hypotenuse
tangent x = (side opposite x)/(side adjacent x)

In the figure, sin A = a/c, cosine A = b/c, and tangent A = a/b.

There are two special triangles you need to know, 45 – 45 – 90 and 30 – 60 – 90 triangles. They are
depicted in the figures below.

The figures show how to find the side lengths of those types of triangles. Besides knowing how to

find the length of any given side of the special triangles, you need to know their trig. ratio values

(they are always the same, no matter the size of the triangle because the trig. ratios depend on the
measure of the angle). A table of these values is given below:

4 LOVELY PROFESSIONAL UNIVERSITY