chapter 4 test 2012 sections 1-4

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Nov 24, 2024

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Pre-Calculus Chapter 4: Trigonometric Functions NAME: DATE: Chapter 4 TEST NON-CALCULATOR Please read all of the directions carefully and show all of your work to receive full credit. Good luck! 1. Evaluate the six trigonometric functions of . Leave your answers as completely simplified expressions. (6 points) sin _____ csc _____ cos _____ sec _____ tan _____ cot _____ 2. Rewrite each degree measure in radians and each radian measure in degrees. (2 points each) a. 94 b. 355 c. 12 d. 3 10 3. Find the value of x and y . Completely simplify your answers. (4 points each) a. b. x = x = y = y = 4. Find the arc length of a sector with a radius of 12 feet and a central angle of 48 . (3 points) 12 10 θ
5. Find the complement and supplement of the angle. (4 points) 5 6 Complement: Supplement: 6. In which quadrant(s) must lie for cos < 0? (2 points) 7. Evaluate the 6 trigonometric functions of 2 . (3 points) sin _____ 2 csc _____ 2 cos _____ 2 sec _____ 2 tan _____ 2 cot _____ 2 8. Given 3 cos 7 , find the exact values for other five trigonometric functions of . Leave your answers as completely simplified expressions. (6 points) sin _____ csc _____ sec _____ tan _____ cot _____ 9. Find the point ( x , y ) on the unit circle that corresponds to the real number t . (2 points each) a. 5 6 t b. 4 3 t  c. 7 4 t
10. If the coordinate 3, 9 lies on the terminal side of , evaluate the 6 trigonometric functions of . Leave your answers as completely simplified expressions. (8 points) sin _____ csc _____ cos _____ sec _____ tan _____ cot _____ 11. Name the reference angle for 7 5  . Sketch both and ’. (4 points) θ θ 12. Evaluate each function: (4 points each) a. 120 tan b. 23 sec 6 c. 4 7 sin d. cot 510 Pre-Calculus Chapter 4: Trigonometric Functions NAME: DATE: Chapter 4 TEST CALCULATOR
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Please read all of the directions carefully and show all of your work to receive full credit. Good luck! 13. Solve the right triangle. Leave your answers rounded to the nearest tenth, where necessary. (4 points) 14. Hurricane Sandy has left a tree broken in my backyard. The top of the tree branches are touching the ground 13 m from the trunk of the tree. The top of the tree also makes a 29 with the ground. How tall was the tree before it was broken? Round your answer to the nearest tenth. (4 points) 15. There is a little girl trapped on the 4 th floor of a building that has caught fire. The 4 th floor is 54 feet off the ground and a fire truck is 25 feet from the building. At what angle does the ladder need to be placed in order for the firefighters to reach the little girl? Round your answer to the nearest tenth. (4 points) 16. An airplane leaves the runway climbing at 18 with a speed of 275 feet per second. Find the altitude of the plane after 1 minute. Round your answer to the nearest tenth. (4 points)
17. The circular blade on a saw rotates at 2400 revolutions per minute and has a diameter of 4 inches. a. Find the angular velocity of the blade in radians per second. (2 points) b. Find the linear velocity of the blade tip in inches per second. Round your answer to the nearest tenth. (3 points) 18. A tire of radius 20 inches rotates 65 times every minute. What is the linear speed in miles per hour to the nearest tenth? (5 points)