applications of trig practice:

16. Let V1 = (2, -6) and v2 = (-4, 7). a. Compute v, and v2|. (1 point) b. Compute the unit vectors in the direction of ,| and v2). (1 point)17. let v1 = (-6, 4) and v2 = (-3, 6). Compute the following. a. Vi * V2 (1 point) b. The angle between (v, | and |v2|. (1 point) c. The scalar projection of v1 onto v2. (1 point) d. The projection of v1 onto v2. (1 point)\f1. Graphs of two trigonometric functions are shown below. Part I: Compare the periods of the two functions. (4 points) Part II: The solid graph is the graph of one of the six main trigonometric functions. Which of the six is it? How do you know this? (4 points) Part III: The dotted graph is a transformation of the solid graph. It shows a vertical stretch and a horizontal stretch. What are the two stretch factors for the dotted graph? (4 points) Part IV: Take your answers to Part I and Part II and apply the transformation from Part Ill to generate the function that produces the dotted graph. (6 points)2. Consider the function y = sinx and answer the questions that follow. Part 1: Graph two periods of the function y = sinx . Be sure to identify (with a dot that is larger than the line of the graph) five critical points in the graph. (10 points) NIN+ -3 Part II: Describe the relationship of the graph of the function y = 1.5sin(4x) and the graph of y = sinx . Specifically, how do the amplitude and the period of the function y = 1.5sin(4x) differ from the amplitude and period of the original function, y = sinx? (4 points) Part III: Graph two periods of the function y = 1.5sin(4x) . (10 points)3. Consider the two functions below: F(x) = 2 cos(xx) G(x) = =cos(2x) Part I: In a sentence, compare the amplitudes of the two functions. (4 points) Part II: In a sentence, compare the periods of the two functions. Which function has the larger period? (4 points) Part III: Draw sketches of at least two periods of the two graphs, labeling each of the graphs. You may have to approximate the critical points of one of the graphs. (8 points)For the functions below, state the amplitude, period, phase shift, and vertical translation of the graph for the sinusoid. (8 points for each question) 4. H(x) = -3sin x - +2 With respect to the parent function F(x) = sin(x) : Identify the amplitude, period, and phase shift of the function H(x). (8 points) 5 . G( x ) = 2c05 2x x + 25 - 5 With respect to the parent function F(x) = cos(x) : What are the amplitude, the period, the phase shift, and the vertical shift of the function G(x)? (8 points)6. Explain how the graph of R(x) = -3tan x| is related to the graph of the basic trigonometric function F(x) = tanx . Part I: What kind of reflection does the basic function experience? (2 points) Part II: What is the vertical stretch factor of the function R(x)? (2 points) Part III: What is the horizontal stretch factor of the function R(x)? (4 points) Part IV: What is the period of the function R(x)? (4 points)Use your answers to Parts I through IV to graph the function R(x) = -3tan( 3x]. Part V: What are the equations of the vertical asymptotes of this function? (4 points) Part VI: What are the zeros of this function? (4 points) Part VII: Sketch the graph of the function y = -3tan x . (8 points)