A Mathematics Review

# A Mathematics Review

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## A Mathematics Review

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1. A Mathematics Review Unit 1 Presentation 2

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

3. 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

4. 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)

5. Trigonometry Review • Remember SOHCAHTOA? Opposite Side Pythagorean Theorem for Right Triangles: Hypotenuse Side q Adjacent Side

6. Using Polar Coordinates • To convert from Rectangular to Polar Coordinates (or vice versa), use the following:

7. 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°

8. 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.

9. 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

10. 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