UNIT 6: GRAPHING TRIG AND LAWS Final Exam Review

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

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

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

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 y = sin x y = 3 cos x

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

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

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

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

LAW OF SINES

X

 Now you try: X

LAW OF COSINES

 Example: X 2 = – 2(400)(375)(cos35) X 2 = – cos35 X 2 = X = m X

LAW OF COSINES  Now you try: X

ALL DONE