Graphs of sine and cosine

Here are the rules of graphing sine and cosine graphs:

1. Sine/ Cosine ​​​​​​​

2. Y = a sin (bx + c) + d

3. A = amplitude

4. B = period : 2∏/b

5. (bx+c) = Start: bx+c = 0; End: bx+c = 2∏

6. D = vertical translation; d units

Matrices, and elementary row operations

Elementary row operations:

1.Interchange 2 equations

2. Multiply an equation by a non zero constant

3. Add a multiple of an equation to another equation. 

Trig Identities

The Path to of verifying a trig identity:

You must only use one side, you can not work with bothe sides

Try to; factor, add fractions, square a binomial, create a monomial denominator. 

Look to use fundamental identities, they work best. 

Last resort, try to convert everything to sines and cosines

Trr anything, even mistakes help to solve the problem in the end. 

Converting Polar Coordinates

Converting between Rectangular Equations, (equations that contain x and y) and Polar Equations (equations that utilize r and theta (u) instead). When converting from x and y to r and u, use these equations:

 

x = rcos(u)

y = rsin(u)

 

When converting from r and u to x and y, use these equations:

 

tan(u) = y/x

r^2 = x^2 + y^2 (r squared = x squared + y squared)

 

Partial Fractions

When dealing with partial fractions, it is very important to follow the steps below! If you follow the steps, it will make the partial fraction problems very easy. 

The first step is to multiply by the LCD (least common denominator)

Second you need to distribute

Once you do those two steps, combine the terms

Then factor out the variable

When you do that you need to equate 

Next it is time to solve. 

Most people believe that they are done there, but dont forget to write it as a partial fraction.

Cross Product

The cross product of 2 vectors is not a hard topic. 

1. Make a 3x3 matrix, first column should be the variables i, j, k. Second column should be the values of vector U. Third column should be the values of vector V. 

2. Then take the first 2 rows of the matrix and rewrite them next to it. 

3. Then you multiply the diagonal values going forward (see example below, it is the green portion), and add the values you get from that. 

4. Then you multiply the diagonal values going backward (see example below, it is the purple portion), and subtract these values. 

Limits in Calculus

Limits are the core to calculus. The limit do a function is essential in many topics and situations in calculus. Limits are the building blocks of calculus and here is a link to read more. 

http://www.khanacademy.org/math/differential-calculus/limits_topic