Angle Measurement

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:

  1. \(\pi \,radian=180{}^\circ\)
  2. \(1\,radian=\frac{180}{\pi }\)
  3. \(1{}^\circ =\left( \frac{\pi }{180} \right)\) radian
  4. If D is number of degree, R is the number of radians and G is the number of grade in angle \(\theta\) , then \(\frac{D}{90}=\frac{G}{100}=\frac{2R}{\pi }\)
  5. \(\theta =\frac{1}{r}\) 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

Leave a Comment

Your email address will not be published. Required fields are marked *