9.1 Practice A. Name Date sin θ = and cot θ = to sketch and label the triangle. Then evaluate. the other four trigonometric functions of θ.

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1 .1 Practice A In Eercises 1 and, evaluate the si trigonometric functions of the angle Let be an acute angle of a right triangle. Use the two trigonometric functions 10 sin = and cot = to sketch and label the triangle. Then evaluate 7 the other four trigonometric functions of. In Eercises 6, let be an acute angle of a right triangle. Evaluate the other five trigonometric functions of.. sin =. cos = 6. tan = Describe and correct the error in finding tan of the triangle below. 1 1 In Eercises 8 and, find the value of for the right triangle A parasailor is attached to a boat with a rope 80 feet long. The angle of elevation from the boat to the parasailor is 6. Estimate the parasailor s height above the boat. Round our answer to the nearest tenth. Copright Big Ideas Learning, LLC Algebra Resources b Chapter 1

2 Name Date. Practice A In Eercises 1 6, draw an angle with the given measure in standard position In Eercises 7, match the angle measure with the angle A. B. C. In Eercises 10 1, find one positive angle and one negative angle that are coterminal with the given angle In Eercises 1 18, convert the degree measure to radians or the radian measure to degrees You work ever Saturda in the ard from 8:00 A.M. to 11:0 A.M. Draw a diagram that shows the rotation completed b the hour hand of a clock during this time. Find the measure of the angle generated b the hour hand in both degrees and radians. Compare this angle with the angle generated b the minute hand from 8:00 A.M.to 11:0 A.M. 6 Algebra Copright Big Ideas Learning, LLC Resources b Chapter

3 . Practice A In Eercises 1, evaluate the si trigonometric functions of. 1.. (, ) (, 1).. (, ) (, 6) In Eercises 7, use the unit circle to evaluate the si trigonometric functions of In Eercises 8 1, find the angle s reference angle In Eercises 1 16, evaluate the function without using a calculator. 1. csc tan 16. cos( 10 ) 17. The horizontal distance d (in feet) traveled b a projectile launched at an angle and with an initial speed v (in feet per second) is given b d = v sin. Estimate the horizontal distance (in feet) traveled b a football that is kicked at an angle of 60 with initial speed of v = 80 feet per second. What is the horizontal distance in ards? Round our answers to the nearest tenth. Copright Big Ideas Learning, LLC Algebra Resources b Chapter 01

4 Name Date. Practice A In Eercises 1 and, identif the amplitude and period of the graph of the function In Eercises 6, identif the amplitude and period of the function. Then graph the function and describe the graph of g as a transformation of the graph of its parent function.. g( ) = sin. g( ) = cos. g( ) = sin 6. g( ) = cos 7. Which functions have an amplitude of and a period of? A. = sin B. = cos C. = sin D. = cos 8. The motion of a pendulum can be modeled b the function d = cos 6 t, where d is the horizontal displacement (in inches) of the pendulum relative to its position at rest and t is the time (in seconds). Find and interpret the period and amplitude in the contet of this situation. Then graph the function. In Eercises 1, graph the function.. g ( ) sin = 10. g( ) = cos( + ) 11. g ( ) = sin g ( ) = cos ( + ) In Eercises 1 and 1, write a rule for g that represents the indicated transformations of the graph of f. 1. f ( ) cos ; 1. f ( ) sin ; = translation units down and units left = translation 1 unit up and units right 06 Algebra Copright Big Ideas Learning, LLC Resources b Chapter

5 . Practice A In Eercises 1, graph one period of the function. Describe the graph of g as a transformation of the graph of its parent function. 1. g( ) = tan. g( ) = cot. g( ) = tan. g( ) = cot. Describe and correct the error in finding the period of the function f = ( ) tan. Period: 6. Use the given graph to graph each function. a. f ( ) = sec b. f ( ) = csc = cos = sin In Eercises 7 10, graph one period of the function. Describe the graph of g as a transformation of the graph of its parent function. 7. g( ) = csc 8. g( ) = sec. g 1 ( ) = 10. g ( ) = csc sec Copright Big Ideas Learning, LLC Algebra Resources b Chapter 11

6 Name Date.6 Practice A In Eercises 1, find the frequenc of the function. 1. = sin. = cos 1. = sin. = cos. A middle-c tuning fork vibrates with a frequenc f of 6 hertz (ccles per second). You strike a middle-c tuning fork with a force that produces a maimum pressure of Pascals. Write and graph a sine model that gives the pressure P as a function of the time t (in seconds). In Eercises 6 and 7, write a function for the sinusoid. 6., 7. ( ) (, 1 ) (, ) 7 (, ) 8. The table shows the depth d (in feet) of the water at the end of an inland dock that is located in a saltwater river that is affected b ocean tides. The time t is measured in hours, with t = 0 representing midnight. t Midnight A.M. A.M. 6 A.M. 8 A.M. 10 A.M. Noon d a. Use sinusoidal regression to find a model that gives d as a function of t. b. Predict the depth of the water at the end of the dock at P.M. 16 Algebra Copright Big Ideas Learning, LLC Resources b Chapter

7 .7 Practice A In Eercises 1 6, find the values of the other five trigonometric functions of sin =, 0 < <. tan =, < < 7. 7 sec =, < < 6. cos =, < < cot =, < < 6 csc =, < < In Eercises 7 1, simplif the epression. 7. cos tan 8. sin ( csc 1). tan sin ( ) ( ) 10. sin tan 11. tan csc 1. 1 sin sec 1. Describe and correct the error in simplifing the epression. In Eercises 1 17, verif the identit. 1. tan cot = 1 1. sin sec = ( ) sin + 1 cos tan cos = sin 17. cos csc = cot ( ) cos 18. As the value of sin decreases, what happens to the value of csc? Eplain our reasoning. Copright Big Ideas Learning, LLC Algebra Resources b Chapter 1

8 Name Date Chapter Cumulative Review In Eercises 1 8, order the epression b value from least to greatest. 1., 6, 7 8, , + 1, 8 +,. 6, +, 6,. 8, +,, ,, 6, ,, 8 +, ,, +, , 7, 8, 7, In Eercises 18, find the midpoint between the two points.. ( 17, 0 ), (, 1) 10. (, 1 ), ( 0, 1) 11. ( 11, 1 ), ( 11, 1) 1. ( 1, 10 ), ( 7, ) 1. ( 16, 11 ), ( 10, 7) 1. (, ), (, ) 1. (, 0 ), ( 18, 1) 16. ( 18, 7 ), ( 10, ) 17. ( 1, 1 ), ( 1, 11) 18. (, 7 ), ( 1, ) In Eercises 1 8, find the distance between the two points. 1. ( 17, 1 ), (, 6) 0. ( 7, 1 ), ( 1, 8) 1. ( 8, 8 ), ( 1, 1). ( 16, ), (, 1). (, 1 ), ( 1, 18). ( 11, ), ( 8, 11 ). (, ), ( 18, 16) 6. (, 1 ), ( 17, 1) 7. (, ), ( 7, 1) 8. ( 18, ), ( 0, 17). A sandbo is in the shape of a right triangular prism. Both side lengths are feet, and it is 1. feet tall. a. What is the length of the third side of the sandbo, or hpotenuse of the triangle? Round our answer to the nearest tenth of a foot. b. What is the volume of the sandbo? c. You want to put sand in the sandbo, but ou onl want the sand to be one foot deep. How much sand do ou need? d. Sand costs $1.1 per cubic foot. Use our answer from part (c) to determine how much it will cost to fill the sandbo 1 foot deep. Round our answer to the nearest cent. 0 Algebra Copright Big Ideas Learning, LLC Resources b Chapter

9 Chapter Cumulative Review (continued) In Eercises 0, find the missing side length of the triangle c 1 ft 16 ft b 1 km km. in.. 6 in. a b 0 mi 18 mi... cm 18 cm. m c 6 m a 6. A mirror is in the shape of a right triangle and has side lengths of 6. inches and 7. inches. What is the area of the mirror? Round our answer to the nearest tenth. 7. A flower bo is in the shape of a right triangular prism. Both side lengths are feet, and it is 1 foot tall. a. What is the length of the third side of the flower bo, or hpotenuse of the triangle? Round our answer to the nearest tenth of a foot. b. What is the volume of the flower bo? c. You want to put potting soil in the sandbo, but ou onl want the soil to be 0.7 foot deep. How much soil do ou need? Round our answer to the nearest tenth. d. Potting soil costs $. per cubic foot. Use our answer from part (c) to determine how much it will cost to fill the sandbo 0.7 foot deep. Round our answer to the nearest cent. Copright Big Ideas Learning, LLC Algebra Resources b Chapter 1

10 Name Date Chapter Cumulative Review (continued) In Eercises 8 6, find the circumference of the circle with the given radius or diameter. Leave our answers in terms of. 8. r = inches. r = 17 kilometers 0. d = miles 1. d = 0 centimeters. r = feet. d = 1 millimeters. r = 16 ards. d = meters 6. r = 1 centimeters In Eercises 7, find the area of the circle with the given radius or diameter. Leave our answer in terms of. 7. d = 1 miles 8. r = inches. d = 8 kilometers 0. r = ards 1. r = 1 feet. r = 7 centimeters. d = meters. d = 18 miles. r = ards In Eercises 6 6, evaluate the epression for (a) = and (b) = In Eercises 6 7, simplif the epression e e 66. e e 67. e e 68. 1e e 7 e 6. 8e e e ( e ) 7. ( e ) 7. ( e ) e 7. 6e e e e e e e e 7. e e e The value of a pair of rollerblades (in dollars) can be approimated b the model t = 10(0.8), where t is the number of ears since the pair of rollerblades was new. a. Tell whether the model represents eponential growth or eponential deca. b. Identif the annual percent increase or decrease in the value of the rollerblades. c. Estimate when the value of the rollerblades will be $60. Algebra Copright Big Ideas Learning, LLC Resources b Chapter

11 Chapter Cumulative Review (continued) In Eercises 81, evaluate the logarithm. 81. log log 6 8. log log 8. log log log log log log log 0.. log 0.06 In Eercises 10, epand the logarithmic epression.. log. log7 8. log 6. log 8 7. log 8. log. ln 100. ln 101. ln 10. log 10. log8 10. log In Eercises , condense the logarithmic epression. 10. log7 6 + log ln 6 ln 107. ln 7 + ln log8 log8 10. log + log z log w + 8 log ln + 6 ln log log 11. ln ln + ln 11. log + log 11. ln z ln log + log + log In Eercises simplif the epression, if possible Copright Big Ideas Learning, LLC Algebra Resources b Chapter