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Mathematical Applications For
The Physics Classroom
Algebra and Trigonometry
Algebra – Solving Expressions
• PEMDAS – Order of operations to solve for an
expression.
1.
2.
3.
4.
5.
6.
Parenthesis
Exponents
Multiplication
Division
Addition
subtraction
Solving For Equations
• When solving for a variable inside of an
equation, the order of operations is reversed.
• Example:
2(x+3)2 = 2
(x+3)2 = 1
√[(x+3)2 ] = √(1)
x+3 = √(1)
x = √(1) – 3
x = -2
Trigonometry
• SohCahToa
– Sin θ= opp/hyp
– Cos θ = adj/hyp
– Tan θ = opp/adj
Hypotenuse
Opposite
θ
Adjacent
• Only works for
right triangles
θ
Hypotenuse
Adjacent
Opposite
Law of Sines and Cosines
• Law of Sines
Sin A = Sin B = Sin C
a
b
c
• Law of Cosines
c2 = a2 + b2 – 2ab (cos C)
• These Laws are used on triangles that are not
right triangles.
Example Problems
1. Solve for a
Vf 2 = Vi 2 +2ad
2. Solve for x
6m
x
θ = 30°
3. Solve for c
c
3m
θ = 100°
7m
Example Problems
4. Solve for a
9m
35°
100°
a
5. Solve for y
y
3.5 m
4m
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