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Precalculus 6.1-6.3 Practice Problems Name___________________________________ SHORT ANSWER. Answer the question. SHOW ALL APPROPRIATE WORK! If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. ! 10) θ = radians, A = 62 square meters, r = ? 6 Draw the angle. 1) 135° 2) - 3! 4 Solve the problem. 11) A gear with a radius of 8 centimeters is turning at ! radians/sec. What is the linear 3 Convert the angle to a decimal in degrees. Round the answer to two decimal places. 3) 75°56'51'' speed at a point on the outer edge of the gear? Convert the angle to D° M' S'' form. Round the answer to the nearest second. 4) 51.46 ° In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. 12) ( 4 , 9 If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. 5) r = 15.0 inches, θ = 30°, s = ? 65 ) 9 Find tan t. Find the exact value. Do not use a calculator. 13) sin 2! Solve the problem. 6) For a circle of radius 4 feet, find the arc length s subtended by a central angle of 60 °. Round to the nearest hundredth. 14) tan ! 15) cot 3! 2 7) The minute hand of a clock is 5 inches long. How far does the tip of the minute hand move in 55 minutes? If necessary, round the answer to two decimal places. 16) sin (- ! ) 2 Convert the angle in degrees to radians. Express the answer as multiple of ". 8) 160° 17) cos (-!) 18) sec ! 4 Convert the angle in radians to degrees. 8! 9) 9 Find the exact value of the expression if θ = 45°. Do not use a calculator. 19) f(θ) = cos θ Find 11f(θ). Find the exact value. Do not use a calculator. 20) cos 60 ° 1 Solve the problem. 35) If sin θ = 0.8 , find the value of sin θ + sin (θ + 2!) + sin (θ + 4!). 21) sec ! 3 Find the exact value of the expression if θ = 30°. Do not use a calculator. 22) g(θ) = cos θ Find g(2θ). 23) f(θ) = cos θ Name the quadrant in which the angle θ lies. 36) tan θ > 0, sin θ < 0 37) cot θ < 0, Find 3f(θ). cos θ > 0 Find the exact value of the expression if θ = 60°. Do not use a calculator. 24) f(θ) = sin θ Find 4f(θ). Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. 38) sec2 70° - tan2 70° Find the exact value. Do not use a calculator. 25) cos 14! 3 Find the exact value of the indicated trigonometric function of θ. 39) csc θ = - 7 , θ in quadrant III Find cot θ. 4 26) sin 495° Find the exact value of the expression. Do not use a calculator. 27) tan 7! + tan 5! 4 4 40) cos θ = 21 , 3! < θ < 2! 29 2 Find cot θ. 41) sin θ = 1 , sec θ < 0 2 Find cos θ and tan θ. 28) cos 120 ° tan 60° Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 42) sin (-60°) A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. 29) (-4, 3) Find sin θ. Solve the problem. 43) If f(θ) = sin θ and f(a) = 30) (- 1 , 1 ) 2 5 Find cos θ. 31) (-4, -1) Find csc θ. value of f(-a). Solve the problem. 32) If sin θ = 0.7, find sin (θ + !). 33) What is the domain of the cosine function? Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 34) tan 570° 2 1 , find the exact 3 Answer Key Testname: 6.1-6.3 PRACTICE16 1) 2) 3) 4) 5) 6) 7) 75.95 ° 51°27'36'' 7.9 in. 4.19 ft 28.8 in. 8! 8) 9 9) 160° 10) 15.39 m 8! cm/sec 11) 3 65 4 12) 13) 14) 15) 16) 17) 18) 19) 20) 0 0 0 -1 -1 2 11 2 2 1 2 21) 2 1 22) 2 23) 3 3 2 24) 2 3 25) - 1 2 3 Answer Key Testname: 6.1-6.3 PRACTICE16 2 26) 2 27) 0 3 28) 29) 2 3 5 30) - 5 29 29 31) - 17 32) -0.7 33) all real numbers 3 34) 35) 36) 37) 38) 3 2.4 III IV 1 39) 33 4 21 40) 20 41) cos θ = 42) - 3 , tan θ = - 2 3 3 3 2 1 43) 3 4