1. UNIT 6: GRAPHING TRIG AND LAWS Final Exam Review

2. TOPICS TO INCLUDE  Parts of a Sine and Cosine Graph  Graphing Sine Functions  Graphing Cosine Functions  Law of Sines  Law of Cosines

3. PARTS OF A SINE AND COSINE GRAPH  All Sine and Cosine graphs have 2 things  AMPLITUDE  MIDLINE  The Amplitude  Determines how HIGH and how LOW the function goes  Can be found at the BEGINNING of a function  The Midline  Determines where the MIDDLE of the graph is  Can be found at the END of the function

4. PARTS OF A SINE AND COSINE GRAPH  Example  Given the function, find the amplitude and the midline y = 2 sinx – 2 Amplitude: 2 Midline: y = -2

5. PARTS OF A SINE AND COSINE GRAPH  You Try:  Use the equation to find the amplitude and midline of the sine or cosine graph 1.y = 5 cos x + 1 2.y = sin x + 4 3.y = 3 cos x

6. GRAPHING SINE FUNCTIONS  Hints for graphing a sine function  Sine functions always  START on the MIDLINE  CROSS the midline at 180° and 360°  Example

7. GRAPHING SINE FUNCTIONS  Now try these: 1.y = 3 sinx – 1 2.y = sinx + 3

8. GRAPHING COSINE FUNCTIONS  Hints for graphing a cosine function  Cosine functions always  Start ABOVE the midline (how far above is determined by the AMPLITUDE)  CROSS the midline at 90° and 270°  Example

9. GRAPHING COSINE FUNCTIONS  Now try these: 1.y = 2 cosx + 2 2.y = 3 cosx – 1

10. LAW OF SINES

11. X

12.  Now you try: X

13. LAW OF COSINES

14.  Example: X 2 = 400 2 + 375 2 – 2(400)(375)(cos35) X 2 = 300625 – 300000cos35 X 2 = 54879.4 X = 234.3 m X

15. LAW OF COSINES  Now you try: X

16. ALL DONE