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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




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:




Sector Area:

Area of segment = Area of sector - Area of triangle:

Area of a triangle

A

B C

a

c b

h




Trigonometric ratios

For the right-angled triangle ABC we have

Hypotenuse

Α Β

C

Adjacent

c

b

α

Op

po

site




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




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




Trigonometric Identities




General Solutions of Trigonometric Equations

{

{

Compound angle trigonometric identities




Double angle trigonometric identities




t-substitution identities

if

then

and

θ

2t

1+t2

1-t2




Sine Rule

In any triangle ABC:

Cosine Rule

In any triangle ABC

A

B C

a

c b

A

B C

a

c b




Trigonometric Functions

Graph Transformations

[ ]




Reciprocal Trigonometric Functions




Inverse Trigonometric Functions

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