b

b

∑ α xi = α

∑ xi

i = a

i = a

b

b

b

∑ xi + ∑ yj = ∑ (xi + yi )

i = a

j = a

i = a

b

c

c

∑ xi + ∑

xi = ∑ xi

i = a

i = b + 1

i = a

b

i

d

j

b

d

i

j

∑

x

∑

y

∑ ∑

y

=

x

i = a

j = c

i = a j = c

• Some common summations:

N

1

∑ i = --N(N + 1 )

i = 1

2

N – 1

N

i

1 – α

1

∑

α

=

---------------,α ≠

for both real and complex α .

1 –

α

= 0

N,α

= 1

i

∞

1

∑

α

i

α

<1 for both real and complex .α For α

≥,1the summation does not

= ------------,

1 –

α

sin θ

=

y

=

1

-

-----------

r

csc θ

cos θ

=

x

=

1

r

-

-----------

r

sec θ

y

y

1

sin θ

tan θ

=

=

=

-

----------

-----------

x

cot θ

cos θ

r

2

= x

2

+ y

2

θ

x

• Graphs of these functions are given below,

Sine - sin

1

-270°

-180°

-90°

0°

90°

180°

270°

360°

450°

-1

1

-270°

-180°

-90°

0°

90°

180°

270°

360°

450°

-1

Tangent - tan

1

-270°

-180°

-90°

0°

90°

180°

270°

360°

450°

-1

1

-270°

-180°

-90°

0°

90°

180°

270°

360°

450°

-1

Secant - sec

1

-270°

-180°

-90°

0°

90°

180°

270°

360°

450°

-1

1

-270°

-180°

-90°

0°

90°

180°

270°

360°

450°

-1

Cosine Law:

c2 = a2 + b2 – 2ab cos θ

c

c

Sine Law:

θ

A

b

a

b

c

------------- =

------------- =

-------------

sin θ A

sin θ B

sin θ

C

θ

θ

C

B