1.

Match each trigonometric function with one of the graphs. - f (2) = CSCI -- f(I) = tanI -. v f (x) = cot I f (I) = SCI H N w X 1. 3 n 2 n -2n 3 n IT 2 2 2 TO V 3 2 X 2 n 2. -2n 2 -3 .4 -53. 2 T -21 X 3 It 2 7 -21 W 2 2 Show your work and explain, in your own words, how you arrived at your answers. Simply entering the equation into a graphing program and reading the results does not demonstrate an understanding of this topic. A- A- IX BIUSX X Styles Font SizeSketch two periods of the graph of the function h (x) = 2 sec (z + 3) . Identify the stretching factor, period, and asymptotes. Enter the exact answers. Stretching factor = Number va la sin (a) Period: P =Enter the asymptotes of the function on the domain [-P, P]. To enter 7, type Pi. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or +1; x -1). The order of the list does not matter. Asymptotes: T = Select the correct graph of h (x) = 2 sec ( T (x + 3) ) 10 y 8 6 4 O -4 -2 2 -2 -8 1012 O X -8 -6 -4 -2 2 4 6 12 + X O 14 -2 -2 -4 -6 -8 -10 X O -8 -6 1 -4 -2 2 4 6 8 12 +Sketch two periods of the graph of the function p {as} = tan (a: E). Identify the stretching factor, period. and asyinptotes. Enter the exact answers. For the number at, either choose 'H' from the bar at the top or type in Pi (with a capital P]. Stretching factor : i n- I:: - Period: P : I Enter the asymptotes of the function on the domain [-P, P]. To enter 7, type Pi. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x - 1). The order of the list does not matter. Asymptotes: > = Select the correct graph of p (x) = tan (x - 8 y O 3 1 Na 4 -6 -88 4 O O - 2- NE 8 -4 -6 -8 CO NO 3 x NA O NO NA -4 -6 -8 8 y 6 2 3 n O 4 NUTH A NO -6 .8A laser rangefinder is locked on a comet approaching Earth. The distance g (x), in kilometers, of the comet after a days, for x in the interval 0 to 24 days, is given by g (x) = 250,000 csc ( T x) a. Select the graph of g (x) on the interval [0, 28]. 1, x 10' 8. x 106 6. x 106 4. x 106 2. x 106 O 0 6 -2. x 100 12 18 24 -4. x 106 -6. x 106 -8. x 10 -1. x 10' 1. x 10' 1 8. x 106 6. x 106 4. x 106 - 2. x 106 O 6 -2. x 106 12 18 24 -4. x 10 -6. x 10 -8. x 106 -1. x 107-1. x 10 8. x 106 6. x 106 4. x 105 2. x 106 O 0 6 -2. x 106 12 18 24 -4. x 10 -6. x 105 -8. x 106 -1. x 10' 1. x 10 8. x 106 6. x 106 4. x 106- 2. x 106 - O -2. x 106 6 X 12 18 24 -4. x 106 -6. x 106 -8. x 100 -1. x 10'b. Evaluate g (4) Enter the exact answer. 9 (4) = Number c. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? The minimum distance between the comet and Earth is Number km which is the Click for List . It occurs at Number days. d. Find and discuss the meaning of any vertical asymptotes on the interval [0, 28]. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x - 1 ). The order of the list does not matter. r = At the vertical asymptotes the comet is Click for ListUse the fundamental identities to fully simplify sin (-x) cos (-x) csc (-2). Enclose arguments of functions in parentheses. For example, sin (2x). sin (a) 00 ? sin (-x) cos (-x) csc (-x) = SIPSimplify the trigonometric expression below by writing the simplified form in terms of cos c. Enclose arguments of functions in parentheses. For example, sin (2x). sin (a) tanr+cot r CSC C =Using the sum and difference of cosines formula, find the exact value of cos 57T 12 Enclose numerators and denominators in parentheses. For example, (a - b) / (1 + n). sin (a) COS 12 Show your work and explain, in your own words, how you arrived at your answer. A - A- IX BIUSXX Styles Font Size Words: 0If sin t = 2: and t is in quadrant I, find the exact value of sin (2 t), cos (2 t), and tan (2 t) algebraically without solving for t. Enclose numerators and denominators in parentheses. For example, (a - b) / (1 + n). sin (a) 00 sin (2 t) = sin (a III cos (2 t) =sin (a) III cos (2 t) = sin (a) tan (2 t) = Show your work and explain, in your own words, how you arrived at your answer for sin (2 t ). A- A- IX BIUS X X Styles Font Size