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# Hurray trigonometry!!

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### Transcript

• 1. Hurray Trigonometry!!
By: Nate Webber
January 9, 2011
• 2. Unit 1
The Unit Circle!
Trig functions!
There is no better way to understanding the trig values of special angles then by knowing the whole Unit Circle!
• 3. Unit 2
Graphs of Trig functions!
Sine, Cosine, and Tangent are like the waves of a radio. Always repeating themselves with the same wave lengths
http://www.analyzemath.com/trigonometry/properties.html
Sine Function : f(x) = sin (x)
• Graph
• 4. Domain: all real numbers
• 5. Range: [-1 , 1]
• 6. Period = 2pi
• 7. x intercepts: x = k pi , where k is an integer.
• 8. y intercepts: y = 0
• 9. maximum points: (pi/2 + 2 k pi , 1) , where k is an integer.
• 10. minimum points: (3pi/2 + 2 k pi , -1) , where k is an integer.
• 11. symmetry: since sin(-x) = - sin (x) then sin (x) is an odd function and its graph is symmetric with respect to the origon (0 , 0).
• 12. intervals of increase/decrease: over one period and from 0 to 2pi, sin (x) is increasing on the intervals (0 , pi/2) and (3pi/2 , 2pi), and decreasing on the interval (pi/2 , 3pi/2).
• Unit 2 (continued)
http://www.analyzemath.com/trigonometry/properties.html
Cosine Function : f(x) = cos (x)
• Graph
• 13. Domain: all real numbers
• 14. Range: [-1 , 1]
• 15. Period = 2pi
• 16. x intercepts: x = pi/2 + k pi , where k is an integer.
• 17. y intercepts: y = 1
• 18. maximum points: (2 k pi , 1) , where k is an integer.
• 19. minimum points: (pi + 2 k pi , -1) , where k is an integer.
• 20. symmetry: since cos(-x) = cos (x) then cos (x) is an even function and its graph is symmetric with respect to the y axis.
• 21. intervals of increase/decrease: over one period and from 0 to 2pi, cos (x) is decreasing on (0 , pi) increasing on (pi , 2pi).
• Unit 2 (continued)
http://www.analyzemath.com/trigonometry/properties.html
Tangent Function : f(x) = tan (x)
• Graph
• 22. Domain: all real numbers except pi/2 + k pi, k is an integer.
• 23. Range: all real numbers
• 24. Period = pi
• 25. x intercepts: x = k pi , where k is an integer.
• 26. y intercepts: y = 0
• 27. symmetry: since tan(-x) = - tan(x) then tan (x) is an odd function and its graph is symmetric with respect the origin.
• 28. intervals of increase/decrease: over one period and from -pi/2 to pi/2, tan (x) is increasing.
• 29. Vertical asymptotes: x = pi/2 + k pi, where k is an integer.
• Unit 3
Simplifying Trig Expressions!
Verifying Trig Identities!
It involves Algebra skillz. There are a lot of formulas to learn in this unit such as:
Sum-Difference Formulas
Reciprocal Identities
Pythagorean Identities
_______________________
• 30. Unit 4
Solving Trig Equations!
Here are a few examples:
Everything that was learned in the last 4 Units were put into this chapter to basically sum everything up 
• 31. Unit 5
Applications of Trig-Right Angles
Oblique Angles!
This Unit was a relaxing unit. There were only a few formulas to understand and the problems were that bad. The fun part about this unit was being able to put it into real life scenarios! Such as finding how tall a building is
Law of Consine!
Law of Sine!
• 32. Unit 5 (continued)
So how do you know when to use which?