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### A Mathematics Review

Unit 1 Presentation 2

Why Review?

- Mathematics are a very important part of Physics
- Graphing, Trigonometry, and Algebraic concepts are used often
- Solving equations and breaking down vectors are two important skills

Graphing Review

- Graphing in Physics done on a Cartesian Coordinate System
- Also known as an x-y plane

- Can also graph in Polar Coordinates
- Also known as an r,q plane
- Very Useful in Vector Analysis

Rectangular vs. Polar Coordinates

Rectangular Coordinate System

X-Y Axes Present (dark black lines)

X Variable

Y Variable

Polar Coordinate System

NO X-Y Axes

R Variable (red lines)

q Variable (blue/black lines)

Trigonometry Review

- Remember SOHCAHTOA?

Opposite Side

Pythagorean Theorem for Right Triangles:

Hypotenuse Side

q

Adjacent Side

Using Polar Coordinates

- To convert from Rectangular to Polar Coordinates (or vice versa), use the following:

Polar Coordinates Example

- Convert (-3.50 m, -2.50 m) from Cartesian coordinates to Polar coordinates.

But, consider a displacement in the negative x and y directions. That is in Quadrant III, so, since polar coordinates start with the Positive x axis, we must add 180° to our answer, giving us a final answer of 216°

Another Polar Coordinates Example

- Convert 12m @ 75 degrees into x and y coordinates.

First, consider that this displacement is in Quadrant I, so our answers for x and y should both be positive.

Trigonometry Review

- Calculate the height of a building if you can see the top of the building at an angle of 39.0° and 46.0 m away from its base.

First, draw a picture.

Since we know the adjacent side and want to find the opposite side, we should use the tangent ratio.

Building Height

39.0°

46.0 m

Another Trigonometry Example

- An airplane travels 4.50 x 102 km due east and then travels an unknown distance due north. Finally, it returns to its starting point by traveling a distance of 525 km. How far did the airplane travel in the northerly direction?

First, draw a picture.

This problem would best be solved using the Pythagorean Theorem.

N

525 km

x km

450 km

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