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This document contains the basic trigonometric functions.
Typology: Study notes
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The word trigonometry is derived from the Greek word โtrigonโ and โmetronโ and it means
measuring the sides of a triangle. Trigonometry was used to solve geometric problems involving
triangles. In the present, it is used in many fields such as,
a) Seismology
b) Designing electric circuits
c) Describing the state of an atom
d) Predicting the heights of tides in the ocean
e) Analyzing a musical tone
The list goes onโฆ
1. Angle
Angle can be measured in clockwise or anticlockwise direction. When measured in clockwise
direction, the angle is negative and angle is positive when measured in anticlockwise direction as
shown in the figure. The ray OA is the initial side and OB is the terminal side in positive angle.
2. Degree and Radian
One full revolution of initial side is 360ยฐ. The angle one degree (1ยฐ) is when the rotation form
initial side to terminal side is (
โ )๐กโ of one revolution. A degree is divided into 60 minutes
and 1 minute is divided into 60 seconds.
1ยฐ = 60' and 1' = 60"
The relationship between degree and radian is as following:
3. Trigonometric functions
sin ๐ฅ = 0 , ๐ฅ = ๐๐, ๐คโ๐๐๐ ๐ ๐๐ ๐๐๐ฆ ๐๐๐ก๐๐๐๐
cos ๐ฅ = 0 , ๐ฅ =
sin ๐ฅ
sec ๐ฅ =
cos ๐ฅ
tan ๐ฅ =
sin ๐ฅ
cos ๐ฅ
cot ๐ฅ =
cos ๐ฅ
sin ๐ฅ
0ยฐ ฯ/6 ฯ/4 ฯ/3 ฯ/2 ฯ 3ฯ/2 2ฯ
sin x 0
cos x 1
tan x 0
Not
defined
Not
defined
4. Sign of trigonometric functions
cos
= cos ๐ฅ
sin
= โ sin ๐ฅ
cot ๐ฅ cot ๐ฆ+ 1
cot ๐ฆ+cot ๐ฅ
2
2
2
2
1 โ๐ก๐๐
2
๐ฅ
1 +๐ก๐๐
2
๐ฅ
2 tan ๐ฅ
1 +๐ก๐๐
2
๐ฅ
2 tan ๐ฅ
1 โ๐ก๐๐
2
๐ฅ
3
3
๐ฅ โ 3 cos ๐ฅ
3 tan ๐ฅโ๐ก๐๐
3
๐ฅ
1 โ 3 ๐ก๐๐
2
๐ฅ
๐ฅ+๐ฆ
2
๐ฅโ๐ฆ
2
๐ฅ+๐ฆ
2
๐ฅโ๐ฆ
2
๐ฅ+๐ฆ
2
๐ฅโ๐ฆ
2
๐ฅ+๐ฆ
2
๐ฅโ๐ฆ
2