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(√2/2)0°(5∏/6)120°(5∏/3)270°(5∏/3)240°(1/2)(√2/2)0°QIII: the unit circle cipher

(√2/2)0°(5∏/6)120°(5∏/3)270°(5∏/3)240°(1/2)(√2/2)0°QIII: the unit circle cipher. Caitlin Bryant, Laura Tinney & Jennifer Davis. MEMORIZE THIS!. Is there an easier way?. Learn the entire Unit Circle in 4 Easy Steps: 1. SAXET, TEXAS 2. QI, QII, QIII, QIV 3. 30+15+15+30

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(√2/2)0°(5∏/6)120°(5∏/3)270°(5∏/3)240°(1/2)(√2/2)0°QIII: the unit circle cipher

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  1. (√2/2)0°(5∏/6)120°(5∏/3)270°(5∏/3)240°(1/2)(√2/2)0°QIII:the unit circle cipher Caitlin Bryant, Laura Tinney & Jennifer Davis

  2. MEMORIZE THIS!

  3. Is there an easier way? • Learn the entire Unit Circle in 4 Easy Steps: • 1. SAXET, TEXAS • 2. QI, QII, QIII, QIV • 3. 30+15+15+30 • 4. Convert to Radians

  4. The unit circle

  5. SOME PRACTICE FOR HOMEWORK • Example Problem on Homework. 1. In ______ the x values are positive and the y values are negative. Answer: QIV QIV = Z Look for the blank at the bottom of the ___Z___ worksheet that 1 corresponds with problem 1 and fill in a Z.

  6. Trifid cipher to teach systems of equations

  7. System of Equations… • Combine equations to eliminate a variable. • Solve for remaining variable. • Replace in an original equation to solve for ‘eliminated’ variable.

  8. 1. (-1,1)

  9. 1. (-1,1)

  10. Completed Grid

  11. The Solution… _____ _____ _____ _____ _____ _____

  12. The Solution… (3,2,1) (2,3,3) (1,3,3) (1,3,2) (1,3,3) (1,1,2) T R I F I D

  13. Frequency Analysis: Breaking the code

  14. What is relative frequency? • The relative frequency for a particular category is the fraction or proportion of the observations in the category. • It is calculated:

  15. How is this method useful in cryptography? • Knowing how often a letter occurs in the English alphabet, we may be able to establish the true identities of the ciphertext characters. • For example, if we discover that the letter “e” occurs 13% of the time (which is the most often), then we can assume the letters that occur the most in the ciphertext may very well be the letter “e” and so on.

  16. Now it’s your turn… • Your homework assignment is to locate a newspaper article and choose 12 consecutive lines to collect data from.

  17. Then take note of how many times each letter in the alphabet occurs. I have made a table for you to use with tally marks.

  18. After each letter is complete, determine the relative frequency that each letter occurs. Remember the formula from earlier! • Now make a histogram to show your results and answer the questions on your worksheet.

  19. Also Part of your homework: • Please read our directions on the worksheets and check for clarity. • Also any constructive criticism would be greatly appreciated. • Keep in mind these worksheets are directed towards high school students. • For the relative frequency worksheet, do not worry about the questions on the back. However, please read over them for clearness. • For the system of equations worksheet, you do not have to complete any of the graphs. • Each worksheet should be completed by the due date.

  20. Your homework is due the Friday after spring break!Please be on time!!

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