Trigonometry : Trigonometry Bindu Krishnakumar
Slide 2 : TRIGONOMETRY Introduction Trigonometry is the branch of mathematics
which deals with the measurement of triangles.
Slide 3 : Angles An angle is formed by
rotating a revolving ray
from one position to another The measure of an angle is
the amount of rotation Positive Angle:- An angle formed by the anticlockwise rotation
Negative Angle:- An angle formed by clockwise rotation
Slide 4 : Measurement of Angles Angle is usually measured in degree and radian measures Degree measure If the circumference of a circle is divided into360 equal parts, the angle subtended by a part at the center is called one degree. 1º =60'(1 degree = 60 minutes)
1'=60?(1 minute = 60 seconds) Radian measure One radian is defined as the angle subtended at
the centre of a circle by an arc of length equal
to the radius Denoted by 1c
p c = 180º 1c = ( 180/ p) º1º = (p/180)c : p c = 180º 1c = ( 180/ p) º1º = (p/180)c Convert into radian
45º
1 º = (p/180)c
45º = 45* p/180
= p/4 Convert into degree
p/15 c
1c = ( 180/ p) º
p /15 = p /15*180/p
= 12º Radian measure of some common angles
Slide 6 : Trigonometric Functions Sine ? = Sin? = opp/hyp = y/r Cosine ? = Cos? = Adj/hyp = x/r Tangent? = Tan? = opp/adj = y/x Cosecant? = Cosec? = hyp/opp = r/y Secant? = Sec? = hyp/adj = r/x Cotangent? = Cot? = adj/opp = x/y o
Slide 7 : I quadrant II quadrant III quadrant IV quadrant All + ve Sine + ve
Cosec Tan
Cot + ve Cos
Sec + ve Signs of trigonometric functions
Trigonometric Identities : Trigonometric Identities cosec?=1/sine ?
sec ?=1/cos ?
cot ?=1/tan ?
tan ?=sin ? /cos ?
Cot=cos ? /sin ? Sin² ? +cos² ? =1
1+tan² ? =sec² ?
1+cot² ?=cosec² ?