8/9/2019 IA Trigonometric Functions(37 40)
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7. TRIGONOMETRIC FUNCTI ONS
Synopsis :
1. Let R. Take an angle of measure radians in the standard
position. Let P(x, y) be a point on the
terminal side of the angle such that OP = r( > 0). Then
i)r
yis called sine of and it is denoted by sin.
ii)r
xis called cosine of and it is denoted by cos
iii)x
y(x 0) is called tangent of and it is denoted by tan.
iv)yx (y 0) is called cotangent of and it is denoted by cot.
v)x
r(x 0) is called secant of and it is denoted by sec.
vi)y
r(y 0) is called cosecant of and it is denoted by cosec.
These six functions (ratios) are called trigonometric functions
(ratios).
2. sin.cosec = 1, sin =
eccos
1, cosec =
sin
1
3. cos.sec = 1, cos =sec
1, sec =
cos
1
4. tan.cot = 1, tan =cot
1, cot =
tan
1
5. =
=
cot
sin
cos,tan
cos
sin
6. sin2 + cos2 = 1,
sin2
= 1 cos2
,cos2 = 1 sin2
7. 1+tan2= sec2, tan2 = sec2 1, sec2 tan2=1.
8. 1 + cot2 = cosec2 , cot2 = cosec2 1,
cosec2 cot2 = 1.
9. sec + tan = tansec
1.
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8/9/2019 IA Trigonometric Functions(37 40)
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Trigonometric Functions
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10. cosec + cot = coteccos
1.
11. The values of the trigonometric functions of some standard
angles :
0 /6 /4 /3 /2 3/2 2
sin 0 1/2 1/ 2 3/2 1 0 1 0
cos 1 3/2 1/ 2 1/2 0 1 0 1
12. Trigonometric functions of 2n + ; nZ
1) sin(2n + ) = sin, cos(2n + ) = cos
2) tan(2n + ) = tan, cot(2n + ) = cot
3) sec(2n + ) = sec, cosec(2n + ) = cosec
13. Trigonometric functions of (), for all values of
1) sin() = sin , 2) cos() = cos ,
3) tan() = tan , 4) cot() = cot ,
5) sec() = sec , 6) cosec() = cosec
14.The values of trigonometric functions of any angle can be
represented in terms of an angle in thefirst quadrant
Let A = n.
2where nZ,
20
. Then
i)
2.nsin = sin , if n is even
= cos , if n is odd
ii) cos
2.n = cos , if n is even
= sin , if n is odd
iii) tan
2.n = tan , if n is even
= cot , if n is odd
iv) cot
2.n = cot , if n is even
= tan , if n is odd
v) sec
2.n = sec , if n is even
= cosec , if n is odd
vi) cosec
2.n = cosec , if n is even
= sec , if n is odd
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