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Mathematical Applications For The Physics Classroom

This resource provides essential tools for mastering algebra and trigonometry in the physics classroom. It covers solving expressions through PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) and demonstrates the reverse order of operations when solving for variables in equations. Key trigonometric concepts such as SohCahToa are presented, explaining sine, cosine, and tangent functions for right triangles. Additionally, it includes the Laws of Sines and Cosines for non-right triangles, along with example problems to reinforce application in real scenarios.

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Mathematical Applications For The Physics Classroom

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  1. Mathematical Applications For The Physics Classroom Algebra and Trigonometry

  2. Algebra – Solving Expressions • PEMDAS – Order of operations to solve for an expression. • Parenthesis • Exponents • Multiplication • Division • Addition • subtraction

  3. 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

  4. Trigonometry • SohCah Toa • Sin θ= opp/hyp • Cos θ = adj/hyp • Tan θ = opp/adj • Only works for right triangles Hypotenuse Opposite θ Adjacent θ Hypotenuse Adjacent Opposite

  5. Law of Sines and Cosines • Law of Sines Sin A = Sin B = Sin C ab c • Law of Cosines c2 = a2 + b2 – 2ab (cos C) • These Laws are used on triangles that are not right triangles.

  6. Example Problems • Solve for a Vf2 = Vi2 +2ad • Solve for x • Solve for c 6 m x θ = 30° c 3 m θ = 100° 7 m

  7. Example Problems • Solve for a • Solve for y 9 m 35° 100° a y 3.5 m 4 m

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