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5/6/14 Obj : SWBAT apply properties of the Law of Sines and Cosines

5/6/14 Obj : SWBAT apply properties of the Law of Sines and Cosines Bell Ringer : HW Requests: 13.3 WS In Class: 13.4 WS Homework : Complete 13.4 WS. Education is Power!. No Half Stepping Just do the work!.

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5/6/14 Obj : SWBAT apply properties of the Law of Sines and Cosines

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  1. 5/6/14 Obj: SWBAT apply properties of the Law of Sines and Cosines Bell Ringer: HW Requests: 13.3 WS In Class: 13.4 WS Homework: Complete 13.4 WS Education is Power! • No Half Stepping • Just do the work!

  2. Law of SinesFind missing parts of any triangle - Works for ANY triangle Not just a right triangle. • http://www.youtube.com/watch?v=ETqe-_plC3Y • Solve a triangle using Law of Sines when: • The measures of 2 ’s and any side are known (AAS or ASA) • The measures of 2 sides & an  opposite one of the sides is known. (SSA) (ambiguous case)

  3. Question: In a triangle, can the sine of an angle be negative, Can the cosine be negative? http://www.youtube.com/watch?v=ETqe-_plC3Y

  4. Law of Sines

  5. Law of Cosines Find missing parts of any triangle - Works for ANY triangle Not just a right triangle. • Solve a triangle using Law of Cosines when: • There are two sides and an included angle, SAS. • There are three sides SSS • In class: pg 494 #6, 10, 18, 38 Exit Ticket: pg 494 #8, 12, 20 • HW:; pg 493 #1-19 odds, 35

  6. Locate the fire

  7. Find the area of the figure

  8. Quadrantal Angles Angles have terminal side and lie on a coordinate axis http://www.youtube.com/watch?v=Tqn6-4W39MI&feature=related

  9. http://www.youtube.com/watch?v=6Qv_bPlQS8E&feature=relmfu http://www.mathsisfun.com/geometry/unit-circle.html

  10. Reference Angles The values of the trig functions for non-acute angles (Quads II, III, IV) can be found using the values of the corresponding reference angles. Definition of Reference Angle Let  be an angle in standard position. Its reference angle is the acute angle formed by the terminal side of  and thehorizontal axis.

  11. Find the reference angle y • Important idea: the triangle is always drawn to the x axis • The reference angle is the POSITIVE ACUTE angle made in the triangle closest to the origin 2 1 1’ x 2’

  12. Find the reference angle y • Find the reference angle for 288 • Draw 288 angle • Draw triangle back to x axis • Find reference angle  x ’ • ’ is what is left over from 360 • 360 – 288 = ’ • = 72

  13. Find the reference angle y • Find the reference angle for 98 • Draw 98 angle • Draw triangle back to x axis • Find reference angle  ’ x • ’ is what is left over from 180 • 180 – 98 = ’ • = 82

  14. Find the reference angle y • Find the reference angle for -55 • Draw -55 angle • Draw triangle back to x axis • Find reference angle x ’  • ’ is what is the same as measured from zero but the positive angle • |-55| = ’ • = 55

  15. y  x Example Find the reference angle for Solution By sketching  in standard position, we see that it is a 3rd quadrant angle. To find , you would subtract 180° from 225 °.

  16. So what’s so great about reference angles? • Well…to find the value of the trig function of any non-acute angle, we just need to find the trig function of the reference angle and then determine whether it is positive or negative, depending upon the quadrant in which the angle lies. • For example, In Quad 3, sin is negative 45° is the ref angle

  17. Example • Give the exact value of the trig function (without using a calculator). • Express the given trigonometric function in terms of the same function of a positive acute angle.

  18. http://www.mathsisfun.com/geometry/unit-circle.html

  19. Examples (Text p 239 #6 & 8) • Express the given trigonometric function in terms of the same function of a positive acute angle.

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