Introduction
- Trigonometry (from Greek trigõnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged during the 3rd century BC from applications of geometry to astronomical studies.
- Trigonometry is most simply associated with planar right angle triangles (each of which is a two-dimensional triangle with one angle equal to 90 degrees). The applicability to non-right-angle triangles exists, but, since any non-right-angle triangle (on a flat plane) can be bisected to create two right-angle triangles, most problems can be reduced to calculations on right-angle triangles. Thus the majority of applications relate to right-angle triangles
What is angle
An angle which has its vertex at the origin and one side lying on the positive x-axis. It can have a measure which positive or negative and can be greater than 360°
- If the direction of rotation is anticlockwise, angle is positive .If the direction of rotation is clockwise,angle is negative
- Once you have made a full circle (360°) keep going and you will see that the angle is greater than 360° .In fact you can go around as many times as you like. The same thing happens when you go clockwise. The negative angle just keeps on increasing
- It can be measured in degrees or radian
Degree and Radian
They both are unit of measurement of angles
Radian: A unit of measure for angles. One radian is the angle made at the centre of a circle by an arc whose length is equal to the radius of the circle.
Degree: If a rotation from the initial side to terminal side is (1/360) of a revolution, the angle is said to have a measure of one degree, written as
1°. A degree is divided into 60 minutes, and a minute is divided into 60 seconds . One sixtieth of a degree is called a minute, written as 1", and one sixtieth of a minute is called a second, written as 1'.
Thus, 1° = 60', 1' = 60"
Relation between Degree and Radian
2π radian = 360 °
π radian= 180 °
1 radian= (180/π) °
| Degree | 30° | 45° | 60° | 90° | 120° | 180° | 360° |
| Radian | π/6 | π/4 | π/3 | π/2 | 2π/3 | π | 2π |
|
Trigonometric Ratio's
In a right angle triangle ABC where B=90° ,we can define six ratio's for the two sides i.e Hypotenuse/Base, Base/Perpendicular,Perpendicular/Base,Base/hypotenuse,Hypotenuse/Perpendicular,Perpendicular/Hypotenuse
Trigonometric ratio's are defined as
- $\sin \theta= \frac {Perpendicular}{Hypotenuse}$
- $cosec \theta= \frac {Hypotenuse}{Perpendicular}$
- $\cos \theta= \frac {Base}{Hypotenuse}$
- $\sec \theta= \frac {Hypotenuse}{Base}$
- $\tan \theta= \frac {Perpendicular}{Base}$
- $\cot \theta= \frac {Base}{Perpendicular}$
Notice that each ratio in the right-hand column is the inverse, or the reciprocal, of the ratio in the left-hand column.
The reciprocal of sin θ is csc θ ; and vice-versa.
The reciprocal of cos θ is sec θ.
And the reciprocal of tan θ is cot θ
These are valid for acute angles.
We are now going to define them for any angles and they are called now the Trigonometric functions.
Also Read
- Notes
- Trigonometry
- Trigonometric functions
- Domain,Range And Graph of trigonometric functions
- Trigonometric Identities
- Trigonometric equations
- Values of Sin 15, cos 15 ,tan 15 ,sin 75, cos 75 ,tan 75
- values of Sin 18, cos 18, tan 18, sin 36,cos 36, Sin 54, cos 72
- Questions
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