What is Angle?
When a ray OA starting from its initial position OA rotates about its endpoint o and takes final position OB
When angle is formed
Positive and Negative Angles
An angle formed by a rotating ray is said to be positive or negative depending on whether its moves anticlockwise or clockwise direction respectively.
Measurement of Angle
Sexagesimal System / Degree Measure
This is also called an English system.
In this system,
1st right angle = 90o
1o = 60’
1’ = 60’’
Centesimal system of Angle Measurement
This is also known as French system.
\({1}’ = {100}’\\ {1}’ = {100}”\).Circular system of Angle Measurement
This is very popularly known as radian system.
In this system, the angle is measured in radian
- A radian is an angle subtended at the centres of a circle by an arc, the whole length is equal to the radius of the circle.
Note:
The numbers of radians in an angle subtended by an arc of the circle at the centres is equl to arc/ radius
\(\theta =\frac{arc}{radius}\)Important Conversions:
- \(\pi \,radian=180{}^\circ\)
- \(1\,radian=\frac{180}{\pi }\)
- \(1{}^\circ =\left( \frac{\pi }{180} \right)\) radian
- If D is number of degree, R is the number of radians and G is the number of grade in angle \(\theta\) , then \(\frac{D}{90}=\frac{G}{100}=\frac{2R}{\pi }\)
- \(\theta =\frac{1}{r}\) Where \(\theta\)= angle sustended by arc of length 1 at centre of circle .
Practice Problems
Illustration 1
Write (3.25) oin D-M-S
3o– 0.25 X 60’ = 3o15’
Illustration 2
Write in (12.3456)g G- M- S
\({{12}^{g}}-34′-56”\)Illustration 3
Correct in to radian 30o
\(30{}^\circ X\,\frac{\pi }{180}=\frac{\pi }{6}\)| Remember \({{\pi }^{c}}=180\) \({{1}^{c\,}}=\frac{180}{\pi }=\frac{180}{22}X7\,=\,57{}^\circ 16’22”\) \({{1}^{c\,}}\simeq 57{}^\circ\) |
Example
Is sin 1 > sin 1o?
Sin 1 = sin 57o
Sin 1o
Hence sin 1 > sin 1o
