Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Convert the degree measure to radians. Leave answer as a multiple of. 1) 30 1) 6 Objective: (3.1) Convert Degrees to Radians (Exact) 2) -450 2) - 5 2 Objective: (3.1) Convert Degrees to Radians (Exact) Convert the radian measure to degrees. Round to the nearest hundredth if necessary. 3) - 5 3) -36 Objective: (3.1) Convert Radians to Degrees (Multiples of ) Convert the degree measure to radians. Leave answer as a multiple of. 4) 650 4) 65 18 Objective: (3.1) Convert Degrees to Radians (Exact) 1
Convert the radian measure to degrees. Round to the nearest hundredth if necessary. 5) 10 3 5) 600 Objective: (3.1) Convert Radians to Degrees (Multiples of ) Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for. 6) 0.2521 6) 14.44 Objective: (3.1) Convert Radians to Degrees (Not Multiples of i) 7) 1 7) 57.30 Objective: (3.1) Convert Radians to Degrees (Not Multiples of i) Find the exact value without using a calculator. 8) cos 2 3 8) - 1 2 Objective: (3.1) Evaluate Trig Function (Exact) 2
9) tan -5 6 9) 3 3 Objective: (3.1) Evaluate Trig Function (Exact) 10) sec -5 4 10) - 2 Objective: (3.1) Evaluate Trig Function (Exact) 11) csc 4 3 11) - 2 3 3 Objective: (3.1) Evaluate Trig Function (Exact) 12) cot -5 6 12) 3 Objective: (3.1) Evaluate Trig Function (Exact) 3
Find the corresponding angle measure in radians. 13) 270 13) 3 2 Objective: (3.1) Give Radian Measure of Angle from Graph Solve the problem. 14) Through how many radians will the hour hand on a clock rotate in 36 hours? 14) 6 Objective: (3.1) Solve Apps: Radian Measure Find the length of an arc intercepted by a central angle in a circle of radius r. Round your answer to 1 decimal place. 15) r = 38.81 ft; = 3 radians 15) 40.6 ft Objective: (3.2) Find Arc Length Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. 16) Find the distance between City A, 60 N and City B, 35 N. (Round to the nearest kilometer.) 2793 km Objective: (3.2) Find Distance Between Cities/Latitude of City 16) 4
17) Find the latitude of Winnipeg, Canada if Winnipeg and Austin, TX, 30 N, are 2234 km apart. 50 N Objective: (3.2) Find Distance Between Cities/Latitude of City 17) Solve the problem. 18) A pendulum swinging through a central angle of 78 completes an arc of length 6.4 cm. What is the length of the pendulum? 4.70 cm Objective: (3.2) Solve Apps: Arc Length 18) 19) A bicycle with a 24-inch wheel (diameter) travels a distance of 1000 feet. How many revolutions does the wheel make (to the nearest revolution)? 159 revolutions Objective: (3.2) Solve Apps: Arc Length 19) 20) A car wheel has a 16-inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward 2 ft? 85.9 Objective: (3.2) Solve Apps: Arc Length 20) 5
Find the area of a sector of a circle having radius r and central angle. Express the answer to the nearest tenth. 21) r = 20.0 m, = 20 21) 69.8 m2 Objective: (3.2) Find Area of Sector Find the exact circular function value. 22) sin 3 4 22) 2 2 Objective: (3.3) Evaluate Circular Function (Exact) Use a table or a calculator to evaluate the function. 23) csc 0.2142 23) 4.704 Objective: (3.3) Evaluate Circular Function (Approximate) 6
The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of. 24) Find sin. 24) - 5 13, 12 13 12 13 Objective: (3.3) Find Circular Function Using Point on Unit Circle 25) Find tan. 25) - 5 13, 12 13-12 5 Objective: (3.3) Find Circular Function Using Point on Unit Circle 7
26) Find tan. 26) 7 25, - 24 25-24 7 Objective: (3.3) Find Circular Function Using Point on Unit Circle Find the value of s in the interval [0, /2] that makes the statement true. 27) tan s = 5.40368606 27) 1.38780765 Objective: (3.3) Tech: Find Angle Given Decimal Function Value Find the exact value of s in the given interval that has the given circular function value. 28) 2, ; sin s = 2 2 28) s = 3 4 Objective: (3.3) Find Angle Given Exact Function Value 8
29) 3 2, 2 ; cos s = 1 2 29) s = 5 3 Objective: (3.3) Find Angle Given Exact Function Value Suppose an arc of length s lies on the unit circle x2 + y2 = 1, starting at point (1, 0) and terminating at the point (x, y). Use a calculator to find the approximate coordinates (x, y). 30) s = 3.1 30) (-0.9991, 0.0416) Objective: (3.3) Find Coordinates of Arc End Point Given Arc Length For the given value of s, decide in which quadrant an angle of s radians lies by evaluating sin s and cos s. 31) s = 33 31) II Objective: (3.3) Find Quadrant Given Arc Length 9
Use the formula = to find the value of the missing variable. t 32) = radian per min, t = 13 min 32) 10 13 10 radians Objective: (3.4) Use Angular Speed Formula Use the formula v = r to find the value of the missing variable. 33) v = 10 ft per sec, r = 1.3 ft 33) 7.7 radians per sec Objective: (3.4) Use Linear Speed Formula Use the formula s = r t to find the value of the missing variable. 34) s = 3 m, r = 7 m, t = 4 sec 34) radian per sec 84 Objective: (3.4) Use Distance Formula Solve the problem. 35) Two pulleys of diameters 6 m and 3 m are connected by a belt. The larger pulley rotates 35 times per min. Find the angular speed of the smaller pulley. 140 radians per min Objective: (3.4) Solve Apps: Linear and Angular Speed 35) 10
36) The radius of the tires of a car is 18 inches, and they are revolving at the rate of 673 revolutions per minute. How fast is the car traveling in miles per hour? 2019 mph 88 Objective: (3.4) Solve Apps: Linear and Angular Speed 36) 37) An object is spinning around a circle with a radius of 16 centimeters. If in 13 seconds a central angle of 1 6 radian has been covered, what is the linear speed of the object? 37) 8 cm per sec 39 Objective: (3.4) Solve Apps: Linear and Angular Speed 38) A ball on the end of a string is spinning around a circle with a radius of 5 centimeters. If in 5 seconds a central angle of 1 radian has been covered, what is the angular speed of the 18 38) ball? 1 radian per sec 90 Objective: (3.4) Solve Apps: Linear and Angular Speed 11