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 Sines Find 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: 1.The measures of 2  ’s and any side are known (AAS or ASA) 2.The measures of 2 sides & an  opposite one of the sides is known. (SSA) (ambiguous case)

6. 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

10. Law of Sines

11. 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: 1.There are two sides and an included angle, SAS. 2.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

13. Locate the fire

14. Find the area of the figure

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

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

18. 18 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. 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 the horizontal axis.

19. Find the reference angle 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 x y 11 1’1’ 22 2’2’

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

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

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

23. 23 Example Find the reference angle for Solution y x  By sketching  in standard position, we see that it is a 3 rd quadrant angle. To find, you would subtract 180° from 225 °.

24. 24 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, 45° is the ref angle In Quad 3, sin is negative

25. 25 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.

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

27. 27 Examples (Text p 239 #6 & 8) Express the given trigonometric function in terms of the same function of a positive acute angle.