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Formula Sheet

Formula Sheet

Pythagorean Theorem

c

Distance Between Two Points

(a, b)

b (x, y)

a

c2 = a2 + b2

p D= (a − x)2 + (b − y)2

PERIMETERS AND AREAS

TRIANGLE

CIRCLE

r

a

c

h b

P =a+b+c

P = 2πr A = πr2

1 A = b·h 2

RECTANGLE

TRAPEZOID

c

b

d

h

b

a

a

A =a·b

P =a+b+c+d a+c ·h A= 2

P = 2a + 2b

Learning outcomes: Author(s):

1

Formula Sheet

VOLUMES AND SURFACE AREAS SPHERE

CYLINDER

r

h r

4 3 πr 3 SA = 4πr2

V = πr2 h

V =

SA = 2πr2 + 2πr · h

RECTANGULAR BOX

CUBE

a

h w

a

l

a

V = lwh

V = a3

SA = 2lw + 2wh + 2lh

SA = 6a2

PYRAMID

CONE

h h r 2

B= area of base

B = πr

1 V = Bh 3

1 V = πr2 h 3

2

Formula Sheet

Trig Functions of Some Special Angles

ANGLE sin(θ) cos(θ) tan(θ) cot(θ) sec(θ) csc(θ)

0

π/6

π/4 π/3 π/2 √ √ 0 1/2 1/ 2 3/2 1 √ √ 1 3/2 1/ 2 1/2 0 √ √ 0 1/ 3 1 3 DNE √ √ DNE 3 1 1/ 3 0 √ √ 1 2/ 3 2 2 DNE √ √ DNE 2 2 2/ 3 1

3

Formula Sheet

Famous Trig Identities tan(θ) =

cos(θ ) sin(θ) , cot(θ) = cos(θ) sin(θ)

sec(θ) =

1 1 , csc(θ) = cos(θ) sin(θ)

cos2 (θ) + sin 2 (θ) = 1 1 + tan2 (θ) = sec 2 (θ)

sin(α + β) = sin(α) cos(β) + cos(α) sin(β) sin(α − β) = sin(α) cos(β) − cos(α) sin(β) cos(α + β) = cos(α) cos(β) − sin(α) sin(β) cos(α − β) = cos(α) cos(β) + sin(α) sin(β)

tan(α + β) =

tan(α) + tan(β ) 1 − tan(α) tan(β )

tan(α − β) =

tan(α) − tan(β ) 1 + tan(α) tan(β )

sin(2θ) = 2 sin(θ) cos(θ) cos(2θ) = cos2 (θ) − sin2 (θ) = 2 cos2 (θ) − 1 = 1 − 2 sin 2 (θ) r ✓ ◆ θ 1 − cos(θ ) sin =± 2 2 r ✓ ◆ θ 1 + cos(θ ) cos =± 2 2 ✓ ◆ θ sin(θ) 1 − cos(θ ) tan = = sin(θ) 1 + cos(θ) 2 4...