Question

Objective: • Graph and describe sinusoidal functions 1. Let x € R and let O be the radian measure of an angle in standard position. (a) Choose a value for z. Then let 0 = x and graph 0. (b) For any value of x, is it possible to find 0 = x? Explain. (c) Choose a value for 0 and graph 0. Is there a real number x that is equivalent to 0? Explain. (d) For any value of 0, is there a real number x that corresponds to 0? (e) Use your work in parts (a)-(d) to jutify the domain of cos(0) and sin(0). 2. Let f(0) = cos(©) and g(0) = sin(0). (a) Graph f(0) and g(0). (b) Graph f(-0) and g(-0). (c) Graph -f(@) and -g(0). (d) Which graphs are identical? What can you conclude about the symmetry of sine cosine? 3. Graph f(0) = cos( 5 – 0) by translating an reflecting the graph of cosine. Can you describe this graph in terms of sine? 4. Let f(0) = 4 sin(20 – 7). (a) What's the domain of f? (b) What's the range of f? (c) List the coordinates of all x-intercepts of the graph of f. (d) Find the coordinates of the y-intercept of f. (e) Find the coordinates of all extrema of f. (f) Graph f as best as you can. 5. Let f(0) = 3 cos(0 – 4). (a) Graph f. (b) Can you find values of A, B, C, DER so that f(0) = A sin(B0+C) + D?

Answer 1

Paoblem. 5. Solution For Given, f60) = 360$ (0-1) fle) = ACOB(B16-6)) Amplitude =A period 21 B Horizontal shift - 0 FLO) = 3 Cop(1.40-1) Amplitude period = 217 Horizontal shift - + a) Graph OF $10) = 300plo-) my (1/3) 191,3) >X . 77 4 1-2,3) -3) 5) P(O) = 3 20$ (644!] +0= A COB (Be+c)+D where A = 3 B = 3 c = -la D=0