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www.ibmaths4u.com ©2014 IBmaths4u.com ®.The information provided on this document is for educational purposes and its accuracy is not guaranteed. Content
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Page 1
r
r
r
1 rad
Trigonometry
Degree measurement of angles
One degree (1o) can be defined as
of one full revolution
1o degree has 60’ minutes
1’ minute has 60’’ seconds
Radian measurement of angles
One radian (1c) is defined as the angle that subtends an arc of length
equal to the radius
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contained on this document is the intellectual property of IBmaths4u.com ® and may not be copied, reproduced, distributed or displayed
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Page 2
Circle Sectors and Segments
A sector of a circle is a region of a circle bounded by a central angle and its
intercepted arc.
The region of a circle bounded by an arc and a chord is called a segment of a
circle.
Arc Length:
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Page 3
Sector Area:
Area of segment = Area of sector - Area of triangle:
Area of a triangle
A
B C
a
c b
h
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contained on this document is the intellectual property of IBmaths4u.com ® and may not be copied, reproduced, distributed or displayed
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Page 4
Trigonometric ratios
For the right-angled triangle ABC we have
Hypotenuse
Α Β
C
Adjacent
c
b
α
Op
po
site
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contained on this document is the intellectual property of IBmaths4u.com ® and may not be copied, reproduced, distributed or displayed
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Page 5
The Unit Circle is the circle with center (0,0) and radius 1 unit.
sinθ
AAss ppooiinntt MM mmoovveess aannyywwhheerree oonn tthhee uunniitt cciirrccllee,,
iittss xx--ccoooorrddiinnaattee iiss ccoossθθ
iittss yy--ccoooorrddiinnaattee iiss ssiinnθθ
tthhee lliinnee sseeggmmeenntt PPQQ iiss ttaannθθ
tthhee lliinnee sseeggmmeenntt KKLL iiss ccoottθθ
cotθ
θ
tanθ
cosθ
M
O
K L
P
Q
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contained on this document is the intellectual property of IBmaths4u.com ® and may not be copied, reproduced, distributed or displayed
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Page 6
Trigonometric table of important angles
Degrees ή
Radians 0 ή 2π
sin 0
√
√
1 0 -1
cos 1 √
√
0 -1 0
tan 0 √
1 √ 0
cot √ 1 √
0 0
Trigonometric table of related angles
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contained on this document is the intellectual property of IBmaths4u.com ® and may not be copied, reproduced, distributed or displayed
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Page 7
Trigonometric Identities
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contained on this document is the intellectual property of IBmaths4u.com ® and may not be copied, reproduced, distributed or displayed
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Page 8
General Solutions of Trigonometric Equations
{
{
Compound angle trigonometric identities
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contained on this document is the intellectual property of IBmaths4u.com ® and may not be copied, reproduced, distributed or displayed
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Page 9
Double angle trigonometric identities
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Page 10
t-substitution identities
if
then
and
θ
2t
1+t2
1-t2
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Page 11
Sine Rule
In any triangle ABC:
Cosine Rule
In any triangle ABC
A
B C
a
c b
A
B C
a
c b
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Page 12
Trigonometric Functions
Graph Transformations
[ ]
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Page 13
Reciprocal Trigonometric Functions
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Page 14
www.ibmaths4u.com ©2014 IBmaths4u.com ®.The information provided on this document is for educational purposes and its accuracy is not guaranteed. Content
contained on this document is the intellectual property of IBmaths4u.com ® and may not be copied, reproduced, distributed or displayed
without IBmaths4u.com ® ‘s express written permission.
Page 15
Inverse Trigonometric Functions
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