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# Exam 1 Study Guide and Review Material Math 113

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This 12 page Study Guide was uploaded by Samantha Jo Butterfield on Thursday February 11, 2016. The Study Guide belongs to Math 113 at University of Wisconsin - Eau Claire taught by Dr. Brisbin in Spring 2016. Since its upload, it has received 44 views. For similar materials see Trigonometry in Mathematics (M) at University of Wisconsin - Eau Claire.

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Date Created: 02/11/16

Math 113 Exam 1 Study Guide Exam 1 will be held in class on Thursday, Feb. 11. Bring a graphing calculator (not a CAS calculator; not the calculator on your phone) a 3 inch by 5 inch notecard (both sides) with whatever you want written on it. To give you a good representation of types of problems that might appear on the exam, this practice exam is about twice as long as the actual exam will be. It will also contain more space for writing your work. 1. True or False: a. The period of tan x is 2π . π π 3π 5π b. tan x is undefined at x=… ,− 2 , 2, 2 , 2 ,… c. π/2 radians is equivalent to 90° . d. If cosθ=−1/2, then cos(−θ)=1/2 . csc x= 1 e. For any angle x where cosx≠ 0 , cosx . 5,y 2. The point ( 6 is on the unit circle in quadrant I. Find y. 1,−2 √ 3. The point ( 3 3 ) is in the unit circle. Find the following. Simplify your answers. a. cosx b. csc x c. cot x 4. Given that 2 √ −√5 sinθ= ,cosθ= , 5 5 find the following. Simplify your answers. tan x a. b. cot x c. sec x sinθ= 2 π <θ<π cosθ 5. Given that 3 and 2 , find . cosθ= −1 π<θ< 3π cscθ 6. Given that 4 and 2 , find . 7. Given that secθ=2 and θ is in quadrant IV, findtanθ . 4 8. Given that cotθ= and cosθ<0 , find sinθ . 3 9. What function is depicted below? A. y=sin x B. y=tanx C. y=secx D. y=csc x 10. The minute hand of a clock is 8 inches long. How far does the tip of the minute hand move in 20 minutes? 11. Melissa has a garden in the shape of a sector of a circle. Its radius is 15 feet and its central angle is 50 degrees. a. Find the area of the garden. Include units with your answer. b. Melissa wants to surround the curved part of her garden with a fence. What length of fence does she need? 12. A race car is driven around a circular track at 180 miles per hour. If the diameter of the track is ½ mile, what is the angular speed of the car? Give your answer in radians per hour and in revolutions (or laps) per hour. 13. For each of the following graphs, write an equation for the function. 14. Starting with the identity 2 2 sin θ+cos θ=1, prove that cot θ+1=csc θ.2 15. In Sydney, Australia, January is the hottest month, with an average high temperature of 27 degrees Celsius. July is the coldest, with an average high temperature of 17 degrees Celsius. Write a sinusoidal function to model the temperature in Sydney. b. Estimate the average high temperature in Sydney in April. 16. The amount of work that Logan has to do ranges between 4 hours and 15 hours per day. It follows a sinusoidal pattern, repeating each week, with a maximum on Wednesdays. Write a function to model the amount of work that Logan has to do, as a function of the day of the week x, where Monday = 1, Tuesday = 2, etc. 17. The current I, in amperes, flowing through an alternating current circuit at time t seconds is π It)=220sin(30πt+ 6),t≥0 a. What is the initial current (at t = 0)? Give an exact answer (not a rounded decimal). b. What is the period? c. What is the maximum current? d. When is the first time when the current reaches its maximum? Give an exact answer (not a rounded decimal). 18. On July 21, 2012, the height of the ocean in Charleston, South Carolina could be modeled by the function 24π y=3.105cos(149 x+11.5)+2.735, where y is the height in feet and x is the number of hours after midnight. a. What was the height of the water at 6 am? b. What was the height of the water at high tide? c. When was the first low tide that day?

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