Trigonometry Functions

SOHCAHTOA

Remember this word for it will help you through any right triangle trigonometry.

SOH

Sin (angle degree) = Opposite side/Hypotenuse

CAH

Cos (angle degree) = Adjacent side/Hypotenuse

TOA

Tan (angle degree) = Opposite side/Adjacent side

Radical and Power Properties

Number of Solutions

Income/Profit Models

Quadratic Models

Estimating Power Model Lines

Traveling Models

Power Model Graphs

Permeter/Area/Volume

Unit 4 Review

The sections in Unit 4 are as follows:

Section 1:
Perimeter/Area/Volume

Section 2:
Power Model Graphs

Section 3:
Traveling calculations

Section 4:
Estimating power model line of best fit

Section 5:
Quadratic Models

Section 6:
Income/Profit Models

Section 7:
How many solutions on a Quadratic Model

Section 8:
Radicals

See the following posts for help on these topics

Quadratic Models

Quadratic Formula:

y = ax^2 + bx + c

(0,c) is the y -intercept for this formula (where the graph crosses the y-axis)

Vertex:
The vertex of the parabola is the maximum or minimum of the curve.

Roots/Zeros:
The roots or zeros of the graph is where the parabola crosses the x-axis.

Sample Quadratic Problem:

A diver on a 3 meter high spring board jumps at an upward velocity of 10 meters/second. Gravity is pulling the diver down into the water. Write a function for height, h, in terms of time, t.

Gravity is -4.9 m/s^2 or -16 m/s^2

h = -4.9t^2 + 10t + 3

Power Model Functions

2 Types of Power Model Functions:

Direct Variation Models:

y = ax^2

y = ax^3

y = ax^n , where n is any positive number

As the value of 'a' gets closer to zero the graph becomes wider.
As the value of 'a' gets farther from zero the graph becomes more narrow.


Inverse Variation Models:

y = ax^-2 = a/x^2

y = ax^-3 = a/x^3

y = ax^-n , where n is any negative number
Or y = a/x^n, where n is any positive number

As the value of 'a' gets closer to zero the graph becomes more narrow.
As the value of 'a' gets farther from zero the graph becomes wider.

Correlation Project

Your correlation Project is due on Thursday November 17 at the time of class. Remember it must be presentable, and if you choose to present your findings you can get up to 5 points extra credit.

Grade Categories:
1. 2 Numerically measurable items = 5 points
2. Table of at least 20 data items = 5 points
3. Scatterplot (labeled) = 5 points
4. Correlation Coefficient = 5 points
5. Strength of Correlation = 5 points
6. Explaination/Conclusion about correlation = 10 points. (more than 1 sentance!)
7. Line of Regression/Line of Best Fit (drawn on scatterplot using centroid and y-intercept and explained) = 5 points
8. Influential Point (must have at least 1) = 5 points
9. Correlation Coefficient without the influential point = 5 points
10. Final Conclusion about your findings = 10 points
11. Overall Project Quality = 10 points

Any questions please ask. Make sure your items are numerically measurable and not ranked!

Data and Correlation Review Packet

Data and Correlation Notes

Spearman's Correlation Coefficient

Spearman's correlation coefficient is a number that tells us how strongly related our ranked items are.

Positive Correlation would be if our coefficient is near the number 1. This means that our items are ranked the same. The scatterplot for positive correlation is composed of points going up and to the right on the graph. The closer they are to a line with slope of 1, the stronger the correlation is; meaning the closer the coefficient will be to the number 1. The more spaced out the points are from that line, the weaker the correlation is; meaning the coefficient will be closer to zero but still positive.

Negative Correlation would be if our coefficient is near the number -1. This means that our items are ranked opposite. The scatterplot for negative correlation is composed of points going down and to the right on the graph. The closer they are to a line with slope -1, the stronger the corelation is; meaning the closer the coefficient will be to the number -1. The more spaced out the points are from that line, the weaker the correlation is; meaning the coefficient will be closer to zero but still negative.

No Correlation would be if our coefficient is the number 0. This means we cannot determine one of the rankings from the other ranking, it is random. The scatterplot for no correlation is composed of points that are randomly on the graph; really spaced out all over.

Spearman's Correlation Coefficient Formula:
r = (6*sum of differences squared) / (number of items ranked *( number of items ranked squared -1))