Math 1330 Precalculus Electronic Homework (EHW 6) Sections 5.1 and 5.2.

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1 Math 0 Precalculus Electronic Homework (EHW 6) Sections 5. and 5.. Work the following problems and choose the correct answer. The problems that refer to the Textbook may be found at in the Online Textbook under the Exercises link in the appropriate section. Record your answers by logging into your CASA account, go to the EMCF link in the top menu bar, selecting the appropriate assignment in the EMCF menu and recording your choices on the EMCF form. You MUST record your answers by the deadline given. No late homework will be accepted. This assignment has 5 questions; your grade will be out of 5 points.. Problem 5.., find csc(t) A. 6 5 B. 6 C. 6 D. 5 5 E. 5 6 F. None of these. Problem 5..6, find cos(t) A. 8 7 B C. 8 6 D E. 8 F. None of these 5. Problem 5..6 a A. B. C. D. E. F. None of these 4. Problem 5..8 a A. E. F. None of these B. C. D. Page of 0

2 5. If 0 t and cos( t) ; evaluate: 4 t t tan t sin 0 sin 6 A. 5 6 B. 6 C. D. 5 4 E. 5 F. None of these 6 6. Which of the following is equivalent to: sin( t) csc( t) cos( t) A. tan( t ) B. cos( t ) C. cot( t ) D. sin( t) E. cos( t) F. None of these Problems 7 0 are matching. Work each problem, then select the correct answer from the answer choices listed to the right of the problems. Note: Answer choices A F may be used more than once or not at all. A. B. sec t 7. Problem 5..0 C. sect 8. Problem 5..4 D. csc t 9. Problem 5..6 E. csct F. tan t Page of 0

3 Section Problem 5.. A. period is ½ units, amplitude is 8 units B. period is 8 units, amplitude is 5 units C. period is 4 units, amplitude is 8 units D. period is 5 units, amplitude is 4 units E. period is 5 units, amplitude is 8 units F. None of the above. Problem 5..4 A. period is units, amplitude is units B. period is units, amplitude is 6 units C. period is units, amplitude is -6 units D. period is 6 units, amplitude is units E. period is units, amplitude is units F. None of the above. Problem 5..6 A. period is units, amplitude is 0 units B. period is units, amplitude is 0 units C. period is units, amplitude is 5 units Page of 0

4 D. period is 0 units, amplitude is units E. None of the above. Problem 5..0 A. A, B, C 4, 0 D8, 0 B. A, C. A 4, D. None of the above B, B 4, C D 4, 0, 0 C,0 D, 0 4. Problem 5..4 A. a. x, b. x c. x 0 B. a. x 0, b. x c. x 0 C. a. x, b. x c. x 0 D. a. x 0, b. x c. x 0 E. None of these 5. Problem 5..6 A. a. x b. x c. x, B. a. x, b. x c. x Page 4 of 0

5 C. a. x b. x, c. x D. a. x, b. x c. x E. a. x b. x c. x, F. None of these 6. Problem 5..8 use the following list rather than the one in the text A. reflect about the y-axis, shift left and up B. reflect about the x-axis, shift left and up C. reflect about the y-axis, shift right and up D. reflect about the x-axis, shift right and up E. reflect about the x-axis, shift right and up F. None of the above 7. Problem 5.. use the following list rather than the one in the text A. shrink (compress) horizontally, shift 8 units right B. shrink (compress) vertically shift 8 units right C. shrink (compress) horizontally, shift 4 units right D. shrink (compress) vertically, shift 4 units right E. None of the above. Page 5 of 0

6 8 & 9 You are strongly urged to: Work these problems completely before looking at any of the answer choices. You will probably need to produce a graph of a trigonometric function on your test. 8. Problem A. Period: Amplitude: 5 B. Period: 5 Amplitude: 6 Phase Shift: None Vertical Shift: None Phase Shift: None Vertical Shift: None C. Period: 6 Amplitude: 5 D. Period: 6 Amplitude: 5 Phase Shift: right Vertical Shift: None Phase Shift: None Vertical Shift: None E. None of these Page 6 of 0

7 9. Problem A. Period: 4 Phase Shift: Right B. Period: 4 Phase Shift: Left Amplitude: 5 Vertical Shift: None Amplitude: 5 Vertical Shift: None C. Period: Phase Shift: right D. Period: 4 Phase Shift: 4 4 Left Amplitude: 5 Vertical Shift: None Amplitude:5 Vertical Shift: None E. None of these Page 7 of 0

8 0. Which of the following is a sine function which has amplitude and period 4? A. y sin x B. y sin4x C. y 4sinx D. y 4 sin x 4 E. None of these. Given the following, determine the maximum, minimum, and x-intercepts in the interval,. y cos x A. Maximum: Minimum: x-intercepts:,0 B. Maximum: / Minimum: / x-intercepts:,,0,0 C. Maximum: Minimum: x-intercepts: 0,, 0, D. Maximum: Minimum: x-intercepts:, E. None of these,0,0 Page 8 of 0

9 . Find the range of the following function: x f x sin 5 A. [-5,5] B. [-,] C. [,8] D. [-8,8] E. [-,-8] F. None of these. The voltage V produced by an alternating current generator is V t 9 sin0 t What are the amplitude and period of V(t)?. A. amplitude: 4.5 period: /60 B. amplitude: 9 period: 60 C. amplitude: 9 period: 0 D. amplitude: 9 period: /60 E. amplitude: 458 period: /60 F. None of these Page 9 of 0

10 4. Scientists believe that the average temperatures at various places on Earth vary from cooler to warmer over thousands of years. At one place on Earth, the highest average temperature is 80 0 and the lowest is Suppose it takes 0,000 years to go from the high to low average and the average temperature was at a high point of 80 0 in year 000. Set up a sinusoidal function Tt ()(where t is time in years) to model this phenomenon. ( ) 0 cos , 000 A. Tt t ( ) 0 cos , 000 B. Tt t C. Tt () 0cos t 70 0, 000 ( ) 0 cos , 000 D. Tt t E. Tt ( ) 0 cos t , 000 F. None of these 5. Let f ( x) Asin( x) D where A and D are real numbers. If the maximum value of f ( x ) is 0 and the minimum value is -, find the value of A) 6 B) -6 C) 0 D) E) 4 F) None of these f. Page 0 of 0

6.4 & 6.5 Graphing Trigonometric Functions. The smallest number p with the above property is called the period of the function.

Math 160 www.timetodare.com Periods of trigonometric functions Definition A function y f ( t) f ( t p) f ( t) 6.4 & 6.5 Graphing Trigonometric Functions = is periodic if there is a positive number p such