ANALYSIS: FINAL REVIEW
ANALYSIS: FINAL REVIEW
HELPFUL INFORMATION
Trig Graphs:
Amplitude = [pic] * The amplitude is the height of the graph
Frequency = b * The frequency is how many complete graphs you should see
Period = [pic] * The period is how long it takes to complete ONE full cycle
Sin x Cos x
Steps to Graphing a Sin/Cos Curve:
1) State your graphing information:
∗ Altitude: [pic]
∗ Value of: b
∗ Period: [pic]
∗ Your interval between key points: [pic]
2) If there is a shift, take the expression inside the parentheses and set it equal to 0 then solve for x. This will tell you the starting point graph. The value of the shift is your interval.
3) Begin with your starting point and add the interval you found in step 1 to find the next key value. Repeat until you have filled up the positive side of your horizontal axis. Fill up the left side of you axis by subtracting the interval until you have filled up the negative side of your horizontal axis. These are the values for each line of your horizontal axis.
4) Label your horizontal axis.
5) Graph the key points to fit the general behaviors of the sine or cosine graph.
6) Connect the points and label the graph.
Signs of Trigonometric Functions:
*** A Smart Trig Class ***
Quadrant II Quadrant I
[pic] [pic]
Quadrant III Quadrant IV
[pic] [pic]
Reference Angles:
Quadrant I: The reference angle equals the angle
Quadrant II: 180 – angle
Quadrant III: Angle – 180
Quadrant IV: 360 – angle
Law of Sines:
If ABC is a triangle with sides, a, b, and c, then
[pic]
*** To solve an oblique triangle you need to know the measure of at least one side and any two other parts of the triangle.
Law of Cosines:
[pic]
*** Use the Law of Cosines when you ONLY have sides
*** After you use Law of Cosines ONCE then you can use Law of Sines
DeMoirvre’s Theorem:
If [pic]is a complex number and n is a positive integer, then:
[pic]
Example:
Use DeMoivre’s Theorem to find [pic]
*** First convert to trigonometric form: a = -1 b = [pic]
[pic] [pic]
Trigonometric form: [pic]
DeMoirve’s:
[pic]
Cramer’s Rule:
Example:
Use Cramer’s Rule to solve the following system of linear equations:
[pic]
[pic]
[pic]
Arithmetic Sequences: Uses addition / subtraction to change from term to term.
* If the terms go up then the common difference (d) is positive
* If the terms go down then the common difference (d) is negative
Standard deviation:[pic]
[pic]
1. Do (score – mean)2 for each data value
2. Add all the answers up
3. Divide by how many terms there were
4. Take the square root
ANALYSIS FINAL – FORMULA
Law of Sines Law of Cosines Area of Oblique Triangles
[pic]
Heron’s Area Formula Component form of a vector Magnitude
[pic]
Orthogonal Vectors Trigonometric form of a Complex # DeMoivre’s Thrm
[pic]
Arithmetic Sequences Geometric Sequences Standard Deviation
[pic]
[pic]
Sample % Con. Int. for Sample % Con. Int. for Sample Mean
[pic]
Confidence Coefficients
Confidence Level: 80% 90% 95% 98% 99%
Confidence Coefficient: 1.28 1.65 1.96 2.33 2.58
Unit Circle
[pic]
Pascal’s Triangle
[pic]
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