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Welcome to Trigonometry!

Welcome to Trigonometry! . We’ll be “Getting’ Triggy” with these concepts… 6.1: find exact values of trigonometric functions (5-1) 6.2: find coterminal and reference angles and to covert between units of angle measure (5-1)

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Welcome to Trigonometry!

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  1. Welcome to Trigonometry! We’ll be “Getting’ Triggy” with these concepts… • 6.1: find exact values of trigonometric functions (5-1) • 6.2:find coterminal and reference angles and to covert between units of angle measure (5-1) • 6.3: solve for missing values in right triangles (5-4, 5-5) • 6.4:use the law of sines and cosines and corresponding area formulas (5-6) • 6.5:use the ambiguous case of the law of sines to solve problems (5-7)

  2. Warm-up:

  3. 6.2 find coterminal and reference angles and to convert between units of angle measure (5-1) In this section we will answer… • How are angles measured in Trig? • What are the different units of angle measure within degree measurement? • What does it mean for angles to be co-terminal? • How can I find a reference angle?

  4. Angles and Their Measures • From Geometry:

  5. In Trig • Angles are always placed on the coordinate plane. • The vertex is at the origin and one side (theinitial side) lies along the x-axis. • The other side (the terminal side) lies in a quadrant or on another axii. • This is called Standard Position.

  6. Angle Direction: • Angles can be measured in two directions. • Counter-clockwise is positive. • Clockwise is negative.

  7. Degree Measurement: • One full rotation = _________________. • The circle has been cut into 360 equal pieces. • Measure of less than a degree can be shown 2 ways: • Decimal pieces: 55.75º • Minutes and seconds: used for maps 103º 45’ 5” • Each degree is divided into 60 minutes. • Each minute is divided into 60 seconds. • 1º = 60’ = 3600”

  8. Change -16.75

  9. Change 183.47 P280 #19 – 65 odd

  10. Change 29º 30’ 60”

  11. Change 103º 12’ 42”

  12. Degrees on the Coordinate Plane: Unit Circle

  13. Translating Rotations to Degrees • Give the angle measure which is represented by each rotation: • 5.5 rotations clockwise • 3.3 rotations counterclockwise

  14. Coterminal Angles • Angles in standard position which share the same terminal side. 150º - 210º

  15. Finding Coterminal Angles • Simply add or subtract 360º as many times as you like. • To write a statement to find EVERY angle coterminal with a certain angle:

  16. Identify all the angles which are coterminal with the given angle. Then find one positive and one negative coterminal angle. • 86º • 294º

  17. If each angle is in standard position, a) State the quadrant in which the terminal side lies b) Determine a coterminal angle that is between 0º and 360º. • 595º • -777º

  18. Reference Angle: • The acute angle formed by the terminal side of an angle in standard position and the x-axis. • The quickest route to the x-axis.

  19. Recap: • How are angles measured in Trig? • What are the different units of angle measure within degree measurement? • What does it mean for angles to be co-terminal? • How can I find a reference angle?

  20. Homework: • P280 #19 – 65 odd • Portfoliodue Thursday 4/14

  21. 5-Minute Check Lesson 5-2A

  22. 5-Minute Check Lesson 5-2B

  23. 6.3: solve for missing values in right triangles (5-4, 5-5) In these sections we will answer… How are the 6 trig ratios expressed in geometry? In trig? How can I use these relationships to solve triangle problems?

  24. Right Triangles in Geometry: ∆ ABC Used the 3 basic trig ratios: sin A, cos A and tan A. SOH-CAH-TOA Now we will add 3 reciprocal ratios: csc A, sec A and cot A.

  25. Solving Using Right Triangles:

  26. *Be Careful with Reciprocal Ratios*

  27. Try some more… p 288

  28. Right Triangles in Trig: Angles are in Standard Position in the Unit Circle. 1 1 -1 -1

  29. Try Some… The terminal side of angle θ in standard position contains (8,-15), find the 6 trig ratios. Now find the angle.

  30. If the csc θ = -2 and θ lies in QIII, find all 6 trig values. Now find the angle.

  31. If the tan θ = -2 and θ lies in QII, find all 6 trig values. Now find the angle.

  32. Homework: P 288 #11 – 25 odd P 296 #15 – 45 odd and 49

  33. WARM-UP:

  34. Homework:

  35. 6.1: find exact values of trigonometric functions (5-2/5-3) In this standard we will… • Review the side relationships of 30°-60°-90° and 45°-45°-90° triangles. • Build trig ratios based 30°-60°-90° and 45°-45°-90° triangles.

  36. Special Triangles from Geometry: Build a chart to show all 6 trig ratios.

  37. Special Triangles on the Unit Circle:

  38. 6.3 solve for missing values in right triangles (5-4) In this standard we will answer… • How can right triangle relationships by used to solve problems?

  39. Let’s start with some triangles… • If A = 37º and b = 6, solve the rest of the triangle.

  40. If B = 62º and c = 24, solve the triangle.

  41. The apothem of a regular pentagon is 10.8 cm. Answer the following. • Find the radius of the circumscribed circle. • What is the length of one side of the pentagon? • Find the perimeter of the pentagon. r a = 10.8 cm

  42. p 303 • Mr. Fleming is flying a kite. Ms Case notices the string makes a 70˚ angle with the ground. “I know the string is 65 meters long,” says Ms Case. “I wonder how far is the kite above the ground?” • Ranger Gladd sights a fire from his fire tower in Alvarez National forest. He finds an angle of depression to the fire of 22˚. If the tower is 75 meters tall, how far is the fire from the base of the tower?

  43. Partner Solve: • ONE piece of paper. • One person solves then second person checks and either praises or coaches. • Change jobs. • Do p 301 #1 – 9 all

  44. Homework: • LEARN YOUR SPECIAL TRIANGLES or UNIT CIRCLE! • P 303 #11-29 odd

  45. Homework:

  46. 6.3: solve for missing values in right triangles (5-5) In this section we will answer… What can I do to solve if I don’t know any angles, just sides?

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