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Welcome to Week 1 College Trigonometry

Welcome to Week 1 College Trigonometry. Trigonometry?. What is trigonometry?. Trigonometry?. Tri means three Gon means sides Ometry means measurement. Trigonometry?. Originated with the Egyptians. Trigonometry?. Arabic Trigonometry was developed in order to

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Welcome to Week 1 College Trigonometry

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  1. Welcome to Week 1 College Trigonometry

  2. Trigonometry? What is trigonometry?

  3. Trigonometry? Tri means three Gon means sides Ometry means measurement

  4. Trigonometry? Originated with the Egyptians

  5. Trigonometry? Arabic Trigonometry was developed in order to observe holy days on the correct days in all parts of the Islamic world

  6. Trigonometry? There was also a need for non-navigators to be able to travel to Mecca each year and return successfully

  7. Trigonometry? In the early 9th century AD, Muhammad ibn Mūsā al-Khwārizmī wrote the first modern trig book (blame him…)

  8. Trigonometry? The trig functions and natural exponentials and logarithms we study in this class are needed in most formulas used to describe how our complicated universe works

  9. Trigonometry? astronomy banking electronics biology atoms forensics construction ...

  10. Trigonometry! At last! Something USEFUL!!!

  11. Questions?

  12. Angles To study triangles, let’s start with one corner: an angle

  13. Angles A ray is half of a line it has an origin the other end stretches on forever origin

  14. Sun rays

  15. Death rays

  16. Angles Real-life death rays: Gamma rays Cosmic rays

  17. Angles If two rays start at the same origin, they form an “angle”

  18. Angles Their point of common origin is called the “vertex” vertex

  19. Angles Angles are usually represented by lowercase Greek letters: α, β, θ θ

  20. Angles Angles have an initial (beginning) side and a terminal (ending) side terminal θ initial

  21. Angles The “standard position” for an angle: vertex at origin and initial side along x-axis θ x (0,0)

  22. Angles Positive angles - counterclockwise rotation from initial side θ

  23. Angles Negative angles - clockwise rotation from initial side θ

  24. ANGLES IN-CLASS PROBLEMS Which of the following graphs represent negative angles?

  25. Angles Remember graph paper?

  26. Angles Graph paper is made of angles:

  27. Angles Graph paper is split into 4 quadrants:

  28. Angles The quadrants move counterclockwise around the grid just like positive angles I II III IV

  29. Angles An angle with a terminal side in a quadrant "lies" in that quadrant I II III IV

  30. ANGLES IN-CLASS PROBLEMS Which quadrant does each angle lie?

  31. Angles An angle with a terminal side along any axis is called “quadrantal”

  32. Angles Angles are measure by determining the amount of rotation from the initial side to the terminal side θ

  33. Angles A degree, symbolized by ° measures angles 23° θ

  34. ANGLES IN-CLASS PROBLEMS Which of the graphs represents the angle θ = –45º in standard position?

  35. Angles Types of angles:

  36. ANGLES IN-CLASS PROBLEMS Classify the angle:

  37. ANGLES IN-CLASS PROBLEMS Classify the angle: 168º 42º 90º 180º 263º

  38. Angles A “reference angle” is a positive acute angle θ° formed by the terminal side of a nonacute angle θ and the x-axis

  39. ANGLES IN-CLASS PROBLEMS Which is the reference angle?

  40. ANGLES IN-CLASS PROBLEMS Co-terminal angle θ ± k•360° Which angle is co-terminal to 275º? a) 85º b) –85º c) –55º d) 55º

  41. ANGLES IN-CLASS PROBLEMS Complementary - two positive angles whose sum = 90° Find the complementary angle to 32º a) 148º b) –32º c) 328º d) 58º

  42. ANGLES IN-CLASS PROBLEMS Supplementary - two positive angles whose sum = 180° Find the supplementary angle to 32º: a) 148º b) –32º c) 328º d) 58º

  43. ANGLES IN-CLASS PROBLEMS Explementary - two positive angles whose sum = 360° Find the explementaryangle to 32º: a) 148º b) –32º c) 328º d) 58º

  44. Questions?

  45. RIGHT ANGLE TRIANGLES IN-CLASS PROBLEMS A polygon with three sides and three angles is called _______

  46. Right Angle Triangles A triangle!

  47. RIGHT ANGLE TRIANGLES IN-CLASS PROBLEMS A special triangle has one corner that is a right angle – what is it called?

  48. RIGHT ANGLE TRIANGLES IN-CLASS PROBLEMS The side of the triangle opposite of the right angle is called: __________

  49. Right Angle Triangles

  50. RIGHT ANGLE TRIANGLES IN-CLASS PROBLEMS Given the lengths of two sides of a right triangle, you can calculate the third using ____ a2+ b2 = c2

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