Download College and Engineering Physics Algebra, Trigonometry, and

College and Engineering Physics
Algebra, Trigonometry, and Geometry
Algebra
Trigonometry
Geometry
1
College and Engineering Physics
Algebra, Trigonometry, and Geometry
You need to remember algebra.
Here are some of the basics…
If A + B = C
then A + B − B = C − B
Distributive property
A × (B + C ) = ( A × B ) + ( A × C )
A=C−B
If A × B = C
Commutative properties
then A × B / B = C / B
A+ B = B + A
A=C/B
A× B = B × A
…and similarly for square roots, squares, subtraction and
division except that subtraction and division are NOT
commutative!
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College and Engineering Physics
Algebra, Trigonometry, and Geometry
Here are some other helpful concepts…
If A = C
and B = C
Ratios
If AC = D
and BC = E
then A = B
…even if YOU DON’T KNOW C!
Simultaneous Equations
then
A D
=
B E
…even if YOU DON’T KNOW C!
a1 A + b1 B = c1C
+
a2 A + b2 B = c2C
(da1 + a2 )A + (db1 + b2 )B = (dc1 + c2 )C
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usually we use this in such a way that
one of the coefficients is zero
College and Engineering Physics
Algebra, Trigonometry, and Geometry
When using your calculator, remember the rules of order…
1. P
Parentheses are calculated first.
2. E
Exponentials and roots are calculated next.
3. M
Multiplication and
D
Division are third.
4. A
Addition and
S
Subtraction are last.
5. Within each category, we calculate from left to right.
Please, Excuse My Dear Aunt Sal!
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College and Engineering Physics
Algebra, Trigonometry, and Geometry
sin
II
I
−
1
2
1
3
2
1
2
1
2
1
150o
45o
330o
−
1
cos
1
2
3
2
III
IV
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College and Engineering Physics
Algebra, Trigonometry, and Geometry
Given a right triangle, the trigonometric functions for either
non-right angle are given by the following…
opposite
(o)
hypotenuse
(h)
θ
adjacent
(a)
sin θ =
o
h
cscθ =
h
o
cosθ =
a
h
secθ =
h
a
tan θ =
o
a
cot θ =
a
o
The value of the angle can also be determine by using any two
of the sides. For example,
6
⎛o⎞
tan −1 ⎜ ⎟ = θ
⎝a⎠
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College and Engineering Physics
Algebra, Trigonometry, and Geometry
Here are some basic geometric and trigonometric formulae
which we will use often in this and the next class…
Circumference of a Circle
C = 2πr
Trigonometric Formulae
sin 2 θ + cos2 θ = 1
Area of a Circle
A = πr 2
Surface Area of a Sphere
A = 4πr
Volume of a Sphere
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V = πr 3
3
Quadratic Formula
Surface Area of a Cylinder
(not including end faces)
A = 2πrL
Ax 2 + Bx + C = 0
Volume of a Cylinder
V = πr L
− B ± B 2 − 4 AC
x=
2A
sin( A ± B) = sin A cos B ± cos A sin B
2
cos( A ± B ) = cos A cos B ∓ sin A sin B
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College and Engineering Physics
Algebra, Trigonometry, and Geometry
Here are some useful angle relations…
a
a
b a
a b
b a
a b
b b
b
a
a + b = 180
a + b = 180
a + b = 180
b
a
C
c
a + b + c = 180
a
B
a
a
b
A
c
A
B
C
=
=
sin a sin b sin c
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