TRIGONOMETRY- PPT (Powerpoint Presentation), MATHEMATICS, CLASS X - Class 10 PDF Download

 Page 1


PREPARED BY:-
NAME - MAYURI
CLASS - X-A
ROLL NO - 44
Page 2


PREPARED BY:-
NAME - MAYURI
CLASS - X-A
ROLL NO - 44
Angle measured in standard position. 
Initial side is the positive x – axis which is fixed. 
Terminal side is the ray in quadrant II, which is free 
to rotate about the origin. Counterclockwise rotation 
is positive, clockwise rotation is negative.
Coterminal Angles: Angles that have the same terminal side.
60°, 420°, and –300° are all coterminal.
Degrees to radians: Multiply angle by 
.
180
?
?
3 180
60
? ?
? ?
?
?
radians
Radians to degrees: Multiply angle by .
180
?
?
?
?
45
180
4
? ?
?
?
Arc length = central angle x radius, or . r s ? ?
Note: The central angle must be in radian measure.
Note: 1 revolution = 360° = 2p radians. 
Page 3


PREPARED BY:-
NAME - MAYURI
CLASS - X-A
ROLL NO - 44
Angle measured in standard position. 
Initial side is the positive x – axis which is fixed. 
Terminal side is the ray in quadrant II, which is free 
to rotate about the origin. Counterclockwise rotation 
is positive, clockwise rotation is negative.
Coterminal Angles: Angles that have the same terminal side.
60°, 420°, and –300° are all coterminal.
Degrees to radians: Multiply angle by 
.
180
?
?
3 180
60
? ?
? ?
?
?
radians
Radians to degrees: Multiply angle by .
180
?
?
?
?
45
180
4
? ?
?
?
Arc length = central angle x radius, or . r s ? ?
Note: The central angle must be in radian measure.
Note: 1 revolution = 360° = 2p radians. 
? sin(A) = sine of A = opposite / hypotenuse = a/c
? cos(A) = cosine of A = adjacent / hypotenuse = b/c
? tan(A) = tangent of A = opposite / adjacent = a/b
? csc(A) = cosecant of A = hypotenuse / opposite = c/a
? sec(A) = secant of A = hypotenuse / adjacent = c/b
? cot(A) = cotangent of A = adjacent / opposite = b/a
A
a
b
c
B
C
Page 4


PREPARED BY:-
NAME - MAYURI
CLASS - X-A
ROLL NO - 44
Angle measured in standard position. 
Initial side is the positive x – axis which is fixed. 
Terminal side is the ray in quadrant II, which is free 
to rotate about the origin. Counterclockwise rotation 
is positive, clockwise rotation is negative.
Coterminal Angles: Angles that have the same terminal side.
60°, 420°, and –300° are all coterminal.
Degrees to radians: Multiply angle by 
.
180
?
?
3 180
60
? ?
? ?
?
?
radians
Radians to degrees: Multiply angle by .
180
?
?
?
?
45
180
4
? ?
?
?
Arc length = central angle x radius, or . r s ? ?
Note: The central angle must be in radian measure.
Note: 1 revolution = 360° = 2p radians. 
? sin(A) = sine of A = opposite / hypotenuse = a/c
? cos(A) = cosine of A = adjacent / hypotenuse = b/c
? tan(A) = tangent of A = opposite / adjacent = a/b
? csc(A) = cosecant of A = hypotenuse / opposite = c/a
? sec(A) = secant of A = hypotenuse / adjacent = c/b
? cot(A) = cotangent of A = adjacent / opposite = b/a
A
a
b
c
B
C
30°
45°
60° 45°
2
1
3
1
1
2
3
3
) 30 tan(
2
1
) 30 sin(
2
3
) 30 cos(
?
?
?
?
?
?
3 ) 60 tan(
2
3
) 60 sin(
2
1
) 60 cos(
?
?
?
?
?
?
1 ) 45 tan(
2
2
) 45 sin(
2
2
) 45 cos(
?
?
?
?
?
?
Page 5


PREPARED BY:-
NAME - MAYURI
CLASS - X-A
ROLL NO - 44
Angle measured in standard position. 
Initial side is the positive x – axis which is fixed. 
Terminal side is the ray in quadrant II, which is free 
to rotate about the origin. Counterclockwise rotation 
is positive, clockwise rotation is negative.
Coterminal Angles: Angles that have the same terminal side.
60°, 420°, and –300° are all coterminal.
Degrees to radians: Multiply angle by 
.
180
?
?
3 180
60
? ?
? ?
?
?
radians
Radians to degrees: Multiply angle by .
180
?
?
?
?
45
180
4
? ?
?
?
Arc length = central angle x radius, or . r s ? ?
Note: The central angle must be in radian measure.
Note: 1 revolution = 360° = 2p radians. 
? sin(A) = sine of A = opposite / hypotenuse = a/c
? cos(A) = cosine of A = adjacent / hypotenuse = b/c
? tan(A) = tangent of A = opposite / adjacent = a/b
? csc(A) = cosecant of A = hypotenuse / opposite = c/a
? sec(A) = secant of A = hypotenuse / adjacent = c/b
? cot(A) = cotangent of A = adjacent / opposite = b/a
A
a
b
c
B
C
30°
45°
60° 45°
2
1
3
1
1
2
3
3
) 30 tan(
2
1
) 30 sin(
2
3
) 30 cos(
?
?
?
?
?
?
3 ) 60 tan(
2
3
) 60 sin(
2
1
) 60 cos(
?
?
?
?
?
?
1 ) 45 tan(
2
2
) 45 sin(
2
2
) 45 cos(
?
?
?
?
?
?
) cos(
) sin(
) tan(
A
A
A ?
) sin(
) cos(
) cot(
A
A
A ?
) csc(
1
) sin(
) sin(
1
) csc(
A
A
A
A
?
?
) sec(
1
) cos(
) cos(
1
) sec(
A
A
A
A
?
?
) cot(
1
) tan(
) tan(
1
) cot(
A
A
A
A
?
?
1 ) ( cos ) ( sin
2 2
? ? A A
) ( sec 1 ) ( tan
2 2
A A ? ? ) ( csc ) ( cot 1
2 2
A A ? ?
Quotient identities:
Reciprocal Identities:
Pythagorean Identities: 
Even/Odd identities:
) csc( ) csc(
) sin( ) sin(
A A
A A
? ? ?
? ? ?
) cot( ) cot(
) tan( ) tan(
A A
A A
? ? ?
? ? ?
) sec( ) sec(
) cos( ) cos(
A A
A A
? ?
? ?
Even functions Odd functions Odd functions