1. DegRad        DegRad      DegRad    

2. x y Find the for all angles that are between 0 and 360 degrees (also in include the radian measurements From the chart we get that 45 degrees has a tan = 1  tan is negative in the 2 nd and 4 th quadrants Place a reference angle of 45 degrees in the 2 nd quadrant

3. x y Find the for all angles that are between 0 and 360 degrees (also in include the radian measurements We also need to place a reference angle of 45 in the 4 th quadrant This would give us an angle of 315º (360 – 45) This question would have a final answer of 135º, 315º, radians, or radians

4. Law of Cosines – Finding a Missing Side  Last unit we used the law of sines to find missing sides and angles of a triangle  There is a law of cosines that allows us to find missing sides and angles in problems that the law of sines won’t work A C B a b c  In a law of cosines problem we will have 2 sides and the angle in between them most times

5. Law of Cosines – Finding a Missing Side A C B a b c Law of Cosines These letters need to be the same Can also be written as:

6. Law of Cosines – Finding a Missing Side A C B 50º 20 15 Find side a in the following triangle Whatever side you are looking for always goes by itself on one side of the equals  Plug in what you have and solve (you should get an x 2

7. Law of Cosines – Finding a Missing Side A C B 50º 20 15 Find side a in the following triangle

8. Law of Cosines – Finding a Missing Side A C B 80º 34 23 Find side b in the following triangle 65º We need angle B (the angle between the sides)  180 – 80 – 65 = 35 35º

9. Law of Cosines – Finding a Missing Side C A B 75º 14 43 Find missing side of the triangle, and then use the law of sines to find the missing angles 41.63

10. Law of Cosines – Finding a Missing Side C A B 75º 14 43 Find missing side of the triangle, and then use the law of sines to find the missing angles 41.63 We can now use law of sines to find one of the angles that is missing

11. Law of Cosines – Finding a Missing Side C A B 75º 14 43 41.63

12. Law of Cosines – Finding a Missing Side C A B 75º 14 43 41.63 Now use this angle and the 75 that you were given in the beginning to find the 3 rd angle