Unit T Student Success Sheet (SSS) Graphing Trig Functions (sections )

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1 Unit T Student Success Sheet (SSS) Graphing Trig Functions (sections ) Standards: Trig 4.0, 5.0,6.0 Segerstrom High School -- Math Analysis Honors Name: Period: Thinkbinder Study Group: Reminders: Practice Problems (PQ & PT) are completed in spiral bound notebook only. All pages in spiral notebook should be labeled accordingly: Unit Concept - (title of assignment) Examples: Unit T Concept 1 Practice Quiz Unit T Concept 1-4 Practice Test Website with all video links and resources: kirchmathanalysis.blogspot.com Edmodo Group Codes for class communication: Success means having the courage, the determination, and the will to become the person you believe you were meant to be George Sheehan Concept Mandatory # What we will be learning Practice Practice quiz 1 1 graphing sine and cosine 2 graphing secant and cosecant Practice quiz 2 3 graphing tangent and cotangent Practice quiz 3 Optional Extra practice from textbook This is our final chapter of trigonometry gosh how time flies! We will conclude our time by graphing the six main trigonometric functions. The blanks on page 2 are the most important things you need to know about trig graphs, so study those carefully! A few websites that will help in your understanding (also linked to on blog in MentorMob Playlist)

2 FINAL GRAPH MUST BE CLEARLY SEEN/LABELED/MARKED...I prefer that you do this in colored pencil so it stands out (NO PEN!). Do all work in pencil, and once you are sure of your final answer, go over it in color. Sine/Cosine I need to see 5 key points Cosecant/Secant I need to see original sine or cosine graph + asymptotes + 1 key point (mountain-top or valley-bottom) Tangent/Cotangent I need to see 1 key point + asymptotes THINGS TO KNOW ABOUT TRIGONOMETRIC GRAPHS 1. They are. This means they repeat themselves over and over again. One time through their cycle is called a. The end of one period is always the beginning of the next. When we draw our graphs, I only require you to draw out one period. However, you must know they go on forever and ever. 2. The period for sine, cosine, cosecant, and secant is. This means they go through one cycle while covering units on the x-axis 3. The period for tangent and cotangent is. This means they go through one cycle while covering units on the x-axis. 4. Cosecant and Secant have asymptotes where sine and cosine are equal to zero. This is because they are the of sine and cosine. Thus, if the value of sine is 0, the value of cosecant is 1/0, which is. Undefined = 5. Tangent and Cotangent have asymptotes where their respective ratios are equal to zero. Tangent = sine/cosine, so when cosine = 0, tangent has asymptotes. Tangent's parent asymptotes are thus at and (the two points on the unit circle where the x value is 0). Cotangent = cosine/sine, so when sine = 0, tangent has asymptotes. Cotangent's parent asymptotes are thus at and (the two points on the unit circle where the y value is 0). 6. Sine and cosine graphs have an. Amplitudes are the distance between the highest and lowest points on the graph. They can be found by looking at the equation at the value of. 7. Sine and cosine graphs look like 8. Cosecant and Secant graphs look like 9. Tangent and cotangent graphs look like

3 ---Unit T Student Success Sheet--- Graphing Trig Functions (sections )--- Math Analysis Honors--- [ ( )] WRITING EQUATIONS in graph-able form... First, You must factor out b first! Then, You must decide how to label your scale on your graph so it is easy for you to graph. 1. Find out period. The period for sin/csc and cos/sec is found by using. The period for tan/cot is found by using 2. Find out L/R shift (based on h ) 3. Pick scale that works easily with both period and shift. (usually based on the denominator of the shifted amount; sometimes if the period is also a fraction you have to find the LCD of the two)

4 PQ PROBLEMS: You must complete AT LEAST two graphs of each type (2 sine, 2 cosine, etc). It is suggested you complete all 8 problems for each concept. Print out the graphing chart to fill out for practice. Or, use graph paper and make your own template. Make sure to include all parts of the template if you hand-draw it. Video and Extra problems We will be working out several of these on video together. (#10,14,18,22,26,30) Any problems we don t complete on video can be completed for extra practice at home. Extra Problems # 7,8,11,12,15,16, 19,20,23,24,27,28 are already worked out for you to reference (no video, just work) Odds answer key Evens answer key

5 SAMPLE EQUATION f(x) = a. sin (b (x h) ) + k f(x) = a. cos (b (x h) ) + k amplitude period Plot parent points (5 total) a 2π b 1. plot beginning and end SINE GRAPHS **starts and ends at 0 1 mark = 1 mark = 2. plot middle 3. plot the midpoints of each segment **PLOT PARENT POINTS IN PENCIL **PLOT SHIFTED POINTS IN DIFFERENT COLOR COSINE GRAPHS **starts and ends at amplitude **DECIDE HOW YOU WILL LABEL YOUR SCALE BASED ON YOUR SHIFTS AND PERIOD right or left shift up or down shift Based on h Based on k DOMAIN X-values (interval notation) (-, ) - always (-, ) - always RANGE y-values (interval notation) Depends on amplitude and shifts [, ] Depends on amplitude and shifts [, ]

6 SAMPLE EQUATION **you will be sketching the corresponding sine and cosine graph first, so follow the same steps! amplitude a f(x) = a. csc (b (x h) ) + k f(x) = a. sec (b (x h) ) + k period Plot parent points (5 total) 2π b 1. plot beginning and end 1 mark = 1 mark = SINE GRAPHS **starts and ends at 0 will graph COSECANT 2. plot middle 3. plot the midpoints of each segment **PLOT PARENT POINTS IN PENCIL **PLOT SHIFTED POINTS IN DIFFERENT COLOR COSINE GRAPHS **starts and ends at amplitude will graph SECANT **DECIDE HOW YOU WILL LABEL YOUR SCALE BASED ON YOUR SHIFTS AND PERIOD right or left shift Based on h up or down shift Based on k k will always be 0 for us in this class k will always be 0 for us in this class INVERSE GRAPH You will have a sketch of the corresponding sine or cosine graph in light pencil, and then you will graph the reciprocal function in dark pencil based on the following requirements: 1. vertical asymptotes where the graph crosses the x-axis. X= + n (1 st one) + (½ the period)n 2. Draw graph (looks like a bunch of parabolas) on the mountains and valleys of the reciprocal graph 1. vertical asymptotes where the graph crosses the x-axis. X= + n (1 st one) + (½ the period)n 2. Draw graph (looks like a bunch of parabolas) on the mountains and valleys of the reciprocal graph DOMAIN X-values (interval notation) Depends on asymptotes. Write domain as x asymptotes Depends on asymptotes. Write domain as x asymptotes RANGE y-values (interval notation) Depends on amplitude and shifts (-, ] U [, ) Depends on amplitude and shifts (-, ] U [, )

7 f(x) = a. tan (b (x h) ) + k f(x) = a. cot (b (x h) ) + k SAMPLE EQUATION amplitude Tangent and cotangent graphs do not have amplitudes If a is positive, the graph will go uphill If a is positive, the graph will go downhill period right or left shift up or down shift π b Based on h *This shift is taken into account with your asymptotes (below) Based on k 1 mark = 1 mark = asymptotes b(x-h) = π/2 b(x-h) = -π/2 b(x-h) = 0 b(x-h) = π X= + n (1 st one) + (the period)n X= + n (1 st one) + (the period)n Plot parent points (5 total) 1. plot beginning and end asymptotes TANGENT GRAPHS 2. plot middle point, based on h and k (tangent starts at (0,0), while cotangent starts at ( π/2, 0) 3. Draw graph going uphill or downhill, as decided based on a **DECIDE HOW YOU WILL LABEL YOUR SCALE BASED ON YOUR SHIFTS AND PERIOD COTANGENT GRAPHS DOMAIN X-values (interval notation) Depends on asymptotes. Write domain as x asymptotes Depends on asymptotes. Write domain as x asymptotes RANGE y-values (interval notation) (-, ) - always (-, ) - always

8 Unit T Practice Test Worked out answer key and video answer key available See kirchmathanalysis.blogspot.com for answer keys and extra videos! Use the same directions from the PQ problems for each concept to solve these in order to prepare for the test. Answer key is posted online only at kirchmathanalysis.blogspot.com Worked out answer key available

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