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Basics of Angles


    what you'll learn...

Overview

 »  Angle is measured in degree or radian

 »  Right Angle : 90

 »  Complementary Angles : pair of angles with sum 90

 »  Straight Angle : 180

 »  Supplementary Angles : pair of angles with sum 180

Angle

Before starting with Trigonometry, let us revise the basics required to understand that.

definition of angle

An angle is the measure of rotation between two lines.

angle of a line

An angle for a given line in a coordinate system is, the angle from the x-axis to the line, measured in anti-clockwise direction.

Degree and Radian

An angle is measured in degree or radian.

definition of degree

The measure of angle, "degree" is defined by -- Rotation by a full circle is graded into 360 degrees.

From the figure, one should understand.

 •  The angles are measured with respect to the +ve x-axis.

 •  The graded angles are represented for 20,40,60,.

 •  A line making an angle 30 is shown.

definition of radian

The measure of angle, "radian" is defined by -- 1 radian = angle subtended in a circle, by the arc of length equaling the radius.

From the figure, one should understand

 •  radius of the circle is shown in red dotted line. An arc having length equal to radius of the circle is shown in red dotted arc.

 •  The radian measures 1,2,3 radians are marked

 •  The y-axis at 90 angle is at π2 radian.

 •  the -ve x-axis at 180 angle is at π radian.

 •  the full-circle subtends 2π radian or 360 angle.

 •  line making 30 angle is shown and the angle in radians is π6.

Positive and Negative Angles

positive negative angle of a line

An angle is positive if it is measured in counter-clockwise direction.

The figure shows +30

An angle is negative if it is measured in clockwise direction.

The figure shows -60

angles positive and negative

The measure of angle PQR is -30.

The angle is measured from PQ¯ to QR¯, in clockwise direction.

Some Standard Angles

right angle

Right angle is angle of measure 90 or π2 radian. Note 90=π2 radian

straight angle

Straight angle is angle of measure 180 or π radian.

complementary angles

Pair of angles having sum 90 are called complementary angles.

The word "complementary" is derived from the word "complete". When one angle completes the right angle with another angle, the angles are called complementary angles.

supplementary angles

Pair of angles having sum 180 are called Supplementary Angles.

The word "supplement" means "comes as an addition".
In a straight line the pair of supplementary angles come together.

The two angles 52 and 38 are complementary angles.

The two angles 92 and 88 are supplementary angles.

Summary

Basics of Angles to learn trigonometry :

 •  Angles are measured in degrees and radians.

 •  Right angle and Straight Angle.

 •  Complementary and Supplementary angles.

Angle: For two line segments or rays with common initial point, the amount of rotation in counter clockwise direction from one to another is the angle.

Degree: Rotation by a full circle is graded as 360 and angles are measured in that graded scale.

Radian: Rotation by the length of radius along the arc of a circle, is 1 radian. Angles are measured in proportion to the 1 radian measure.

Right Angle: Angle of 90 or π2 radian.

Straight Angle: Angle of 180 or π radian.

Complementary Angles: Pair of angles having sum 90.

Supplementary Angles: Pair of angles having sum 180.


Outline

The outline of material to learn "Basics of Trigonometry" is as follows.

•   Detailed outline of "trigonometry".

    →   Basics - Angles

    →   Basics - Triangles

    →   Importance of Right Angled Triangle

    →   Trigonometric Ratio (Basics)

    →   Triangular Form of Trigonometric Ratios

    →   Introduction to Standard Angles

    →   Trigonometric Ratio of Standard Angles

    →   Trigonometric Identities

    →   Trigonometric Ratios of Complementary Angles