TRIGNOMETRY-FORMULA AND CONCEPTS BY K.H. V.
AN ANGLE: An angle is the amount of rotation of a revolving line w.r.t a fixed straight line (a figure
formed by two rays having common initial point.) The two rays or lines are called the sides of the angle and common initial point is called the vertex of the angle. Rotation of the initial arm to the terminal arm generates the angle. +ve θ • Rotation can be anti clock wise or clockwise. angle • Angle is said to be +ve if rotation is anti clockwise. Initial • Angle is said to be -ve if rotation is clockwise. -ve angle side(arm)
T sid erm e( ina ar l m )
UNITS OF MEASUREMENT OF ANGLES: b) Centisimal system of angles: a) Sexagesimal system:
In sexagesimal system of measurement, the units of measurement are degrees, minutes and seconds. 1 right angle =90 degrees(90o); 1 degree = 60 minutes (60') 1 minute = 60 seconds (60'') 1 right angle =100 grades =100g 1 grade =100 minutes =100' 1' = 100 seconds =100''
c) RADIAN OR CIRCULAR MEASURE : In this system units of measurement is radian.
A radian is the measure of an angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. one radian is denoted by 1c
1 radian =570 161 22'' D B Arc ----r----- A
A radian is a Constant angle. And radians = 1800
AB be the Arc, Let the length of the arc =OA=radius angle AOB =1 radian
RELATIONSHIP BETWEEN DEGREES AND RADIANS: 180 o radians =180o 1 radian= 1c =
1c = 570 17' 45''; 10 =
VIGNAN CLASSES Do You know? When no unit is mentioned with an angle, it is understod to be in radians. If the radius of the circle is r and its circumference is C then C=2πr C/2r =π for any circle Circumference/diameter =π which is constant. π =3.1416(approximately)
radian=0.01746 radian 180 o
(approximately)
x Degree measure i.e. To convert degrees into radians Multiply by 180 o 180 o Degree measure= x Radian measure. i.e. To convert radians into degrees Multiply by
Radian...