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Study Notes IX-XII - Notes & Assignments XI

Assingment trignomatric functions

Angle: - An angle is considered as a figure obtained by rotating a given ray about its initial point (end point)

• The original position of the ray is called the initial side of the angle.

• The final position of the ray is called the terminal side of the angle.

• An angle is called positive if the direction of rotation of ray from initial side to terminal side is anti-clockwise.

• An angle is called negative if the direction of rotation of ray form initial side to terminal side is clockwise.



SYSTEM OF MEASUREMENT OF ANGLES

Sexagesimal or English System

In this system a right angle is divided into 90 equal parts, called degrees.
One degree () is th part of a right angle.
Each degree is divided into 60 equal parts, called minutes
The symbol 1 is used to denote one minute.

Each minute is divided into 60 equal parts, called seconds.
The symbol 1 is use to denote one second

SOME USEFUL POINTS

radians = 1800

Radian
Degrees	300	450	600	900	1800	2700	3600

• When an angle is expressed in radians, the word radian is generally omitted.
• The angle between two consecutive digits in a clock is 30 or radian
• The hour hand rotate through an angle of 30 in one hour (The hour hand completes one rotation in 12hours)
• The minute hand rotates through an angle of 6 in one minute.



• 

        l = length of arc


        r= radius of circle




= angle subtended by arc of length (l) at the centre of the circle

Trigonometric Ratios of Standard Angles

ANGLE( ) à T-RATIO â	0O	30 O	45 O	60 O	90 O
Sin	0				1
cos	1				0
tan	0		1
cosec		2			1
sec	1			2
cot			1		0

• cos = -1, sin =0, cos = 0, sin = -1, cos2 =1, sin2 = 0

• sin² + cos² = 1

• 1 + tan² = sec²

• 1 + cot² = cosec²

• cosec =

• sec =

• tan =

• cot =

• sin = tan . cos

Note: It should be noted that (sin )² is written as sin²

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