Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus Enhanced with Graphing Utilities
65AYUWrite the formula for the distance d from P 1 =( x 1 , y 1 ) to P 2 =( x 2 , y 2 ) . (p. 4)If is an acute angle, solve the equation cos= 2 2 .(pp.472—475)If three sides of a triangle are given, the Law of ________ is used to solve the triangle.If one side and two angles of a triangle are given, which law can be used to solve the triangle? a. Law of Sines b. Law of Cosines c. Either a or b d. The triangle cannot be solved.If two sides and the included angle of a triangle are given, which law can be used to solve the triangle? a. Law of Sines b. Law of Cosines c. Either a or b d. The triangle cannot be solved.True or False Given only the three sides of a triangle. there is insufficient information to solve the triangle.True or False The Law of Cosines states that the square of one side of a triangle equals the sum of the squares of the other two sides, minus twice their product.True or False A special case of the Law of Cosines is the Pythagorean Theorem.In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 9-16, solve each triangle.In Problems 17-32, solve each triangle. a=3 , b=4 , c =40In Problems 17-32, solve each triangle. a=2 , c=1 , B =10In Problems 17-32, solve each triangle. b=1 , c=3 , A =80In Problems 17-32, solve each triangle. a=6 , b=4 , C =60In Problems 17-32, solve each triangle. a=3 , c=2 , B =110In Problems 17-32, solve each triangle. b=4 , c=1 , A =120In Problems 17-32, solve each triangle. a=2 , b=2 , C =50In Problems 17-32, solve each triangle. a=3 , c=2 , B =90In Problems 17-32, solve each triangle. a=12 , b=13 , c=5In Problems 17-32, solve each triangle. a=4 , b=5 , c=3In Problems 17-32, solve each triangle. a=2 , b=2 , c=2In Problems 17-32, solve each triangle. a=3 , b=3 , c=2In Problems 17-32, solve each triangle. a=5 , b=8 , c=9In Problems 17-32, solve each triangle. a=4 , b=3 , c=6In Problems 17-32, solve each triangle. a=10 , b=8 , c=5In Problems 17-32, solve each triangle. a=9 , b=7 , c=10In Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. B =20 , C =75 , b=5In Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. A =50 , B =55 , c=9In Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. a=6 , b=8 , c=9In Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. a=14 , b=7 , A =85In Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. B =35 , C =65 , a=15In Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. a=4 , C=5 , B =55In Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. A =10 , a=3 , b=10In Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. A =65 , B =72 , b=7In Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. b=5 , c=12 , A =60In Problems 33-42, solve each triangle using either the Law of Sines or the Law of Cosines. a=10 , b=10 , c=1543AYU44AYU45AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYU63AYUThe area K of a triangle whose base is b and whose height is h is _______. (p. A15)If two sides a and b and the included angle C are known in a triangle, then the area K is found using the formula K= .The area K of a triangle with sides a , b , and c is K= , where s= .True or False The area of a triangle equals one-half the product of the lengths of two of its sides times the sine of their included angle.5AYU6AYU7AYU8AYU9AYU10AYU11AYU12AYU13AYU14AYU15AYU16AYU17AYU18AYU19AYU20AYUIn Problems 15-26, find the area of each triangle. Round answers to two decimal places. a=2 , b=2 , c=222AYU23AYUIn Problems 15-26, find the area of each triangle. Round answers to two decimal places. a=4 , b=3 , c=6Area of an ASA Triangle If two angles and the included side are given, the third angle is easy to find. Use the Law of Sines to show that the area K of a triangle with side a and angles A,B, and C is K= a 2 sinBsinC 2sinAArea of a Triangle Prove the two other forms of the formula given in Problem 27. K= b 2 sinAsinC 2sinB andK= c 2 sinAsinB 2sinCIn Problems 29-34, use the results of Problem 27 or 28 to find the area of each triangle. Round answers to two decimal places. A= 40 , B= 20 , a=2In Problems 29-34, use the results of Problem 27 or 28 to find the area of each triangle. Round answers to two decimal places. A= 50 , C= 20 , a=3In Problems 29-34, use the results of Problem 27 or 28 to find the area of each triangle. Round answers to two decimal places. B= 70 , C= 10 , b=5In Problems 29-34, use the results of Problem 27 or 28 to find the area of each triangle. Round answers to two decimal places. A= 70 , B= 60 , c=4In Problems 29-34, use the results of Problem 27 or 28 to find the area of each triangle. Round answers to two decimal places. A= 110 , C= 30 , c=3In Problems 29-34, use the results of Problem 27 or 28 to find the area of each triangle. Round answers to two decimal places. B= 10 , C= 100 , b=2Area of a Segment Find the area of the segment (shaded in blue in the figure) of a circle whose radius is 8 feet, formed by a central angle of 70 . [Hint: Subtract the area of the triangle from the area of the sector to obtain the area of the segment.)Area of a Segment Find the area of the segment of a circle whose radius is 5 inches, formed by a central angle of 40 .Cost of a Triangular Lot The dimensions of a triangular lot are 100 feet by 50 feet by 75 feet. If the price of such land is 3 per square foot, how much does the lot cost?Amount of Material to Make a Tent A cone-shaped tent is made from a circular piece of canvas 24 feet in diameter by removing a sector with central angle 100 and connecting the ends. What is the surface area of the tent?37AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYU45AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYUThe amplitude A and period T of f( x )=5sin( 4x ) are __ and ___. (pp. 412—414)The motion of an object obeys the equation d=4cos( 6t ) . Such motion is described as ____ ____. The number 4 is called the ____.When a mass hanging from a spring is pulled down and then released, the motion is called ____ ____ if there is no frictional force to retard the motion, and the motion is called if there is such friction.True or False If the distance d of an object from its rest position at time t is given by a sinusoidal graph, the motion of the object is simple harmonic motion.In Problems 5-8, an object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T , write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up. a=5;T=2 secondsIn Problems 5-8, an object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T , write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up. a=10;T=3 secondsIn Problems 5-8, an object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T , write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up. a=6;T= secondsIn Problems 5-8, an object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T , write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up. a=4;T= 2 secondsRework Problem 5 under the same conditions, except that at time t=0 , the object is at its resting position and moving down.Rework Problem 6 under the same conditions, except that at time t=0 , the object is at its resting position and moving down.Rework Problem 7 under the same conditions, except that at time t=0 , the object is at its resting position and moving down.Rework Problem 8 under the same conditions, except that at time t=0 , the object is at its resting position and moving down.In Problems 13-20, the displacement d (in meters) of an object at time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the maximum displacement from its resting position? (c) What is the time required for one oscillation? (d) What is the frequency? d=5sin(3t)In Problems 13-20, the displacement d (in meters) of an object at time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the maximum displacement from its resting position? (c) What is the time required for one oscillation? (d) What is the frequency? d=4sin(2t)In Problems 13-20, the displacement d (in meters) of an object at time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the maximum displacement from its resting position? (c) What is the time required for one oscillation? (d) What is the frequency? d=6cos(t)In Problems 13-20, the displacement d (in meters) of an object at time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the maximum displacement from its resting position? (c) What is the time required for one oscillation? (d) What is the frequency? d=5cos( 2 t )In Problems 13-20, the displacement d (in meters) of an object at time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the maximum displacement from its resting position? (c) What is the time required for one oscillation? (d) What is the frequency? d=3sin( 1 2 t )In Problems 13-20, the displacement d (in meters) of an object at time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the maximum displacement from its resting position? (c) What is the time required for one oscillation? (d) What is the frequency? d=2cos(2t)In Problems 13-20, the displacement d (in meters) of an object at time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the maximum displacement from its resting position? (c) What is the time required for one oscillation? (d) What is the frequency? d=6+2cos(2t)In Problems 13-20, the displacement d (in meters) of an object at time t (in seconds) is given. (a) Describe the motion of the object. (b) What is the maximum displacement from its resting position? (c) What is the time required for one oscillation? (d) What is the frequency? d=4+3sin(t)21AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYUIn Problems 25-32, use the method of adding y-coordinates to graph each function. f(x)=x+cosxIn Problems 25-32, use the method of adding y-coordinates to graph each function. f(x)=x+cos(2x)In Problems 25-32, use the method of adding y-coordinates to graph each function. f(x)=xsinxIn Problems 25-32, use the method of adding y-coordinates to graph each function. f(x)=xcosxIn Problems 25-32, use the method of adding y-coordinates to graph each function. f(x)=sinx+cosxIn Problems 25-32, use the method of adding y-coordinates to graph each function. f(x)=sin(2x)+cosxIn Problems 25-32, use the method of adding y-coordinates to graph each function. g(x)=sinx+sin(2x)In Problems 25-32, use the method of adding y-coordinates to graph each function. g(x)=cos(2x)+cosxIn Problems 33-38, (a) use the Product-to-Sum Formulas to express each product as a sum, and (b) use the method of adding y-coordinates to graph each function on the interval [ 0,2 ] . f(x)=sin(2x)sinxIn Problems 33-38, (a) use the Product-to-Sum Formulas to express each product as a sum, and (b) use the method of adding y-coordinates to graph each function on the interval [ 0,2 ] . F(x)=sin(3x)sinxIn Problems 33-38, (a) use the Product-to-Sum Formulas to express each product as a sum, and (b) use the method of adding y-coordinates to graph each function on the interval [ 0,2 ] . G(x)=cos(4x)cos(2x)In Problems 33-38, (a) use the Product-to-Sum Formulas to express each product as a sum, and (b) use the method of adding y-coordinates to graph each function on the interval [ 0,2 ] . h(x)=cos(2x)cos(x)In Problems 33-38, (a) use the Product-to-Sum Formulas to express each product as a sum, and (b) use the method of adding y-coordinates to graph each function on the interval [ 0,2 ] . H(x)=2sin(3x)cos(x)In Problems 3338, (a) use the ProducttoSum Formulas to express each product as a sum, and (b) use the method of adding y-coordinates to graph each function on the interval [ 0,2 ] . g(x)=2sinxcos(3x)47AYU48AYU49AYU50AYU51AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU1RE2RE3RE4RE5RE6RE7RE8RE9RE10RE11RE12RE13RE14RE15RE16RE17RE18RE19RE20RE21RE22RE23RE24RE25RE26RE27RE28RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48RE49RE50RE51RE52RE53RE54RE55RE56RE57RE58RE59RE60RE61RE62RE1CT2CT3CT4CT5CT6CT7CT8CT9CT10CT11CT12CT13CT14CT15CT16CT17CT18CT19CT20CT21CT22CT23CT24CT25CT26CT1CR2CR3CR4CR5CR6CR7CR8CR9CR10CR11CR12CRPlot the point whose rectangular coordinates are ( 3,1 ) . What quadrant does the point lie in?To complete the square of x 2 +6x , add ______ .If P=( x,y ) is a point on the terminal side of the angle and also on the circle x 2 + y 2 = r 2 , then tan= ______ .tan 1 ( 1 )= ______ .5AYUTrue or False In the polar coordinates ( r, ) , r can be negative.True or False The polar coordinates of a point are unique.8AYUIn Problems 11-18, match each point in polar coordinates with either A,B,C,orD on the graph. ( 2, 11 6 )10AYU11AYUIn Problems 11-18, match each point in polar coordinates with either A,B,C,orD on the graph. ( 2, 7 6 )In Problems 11-18, match each point in polar coordinates with either A,B,C,orD on the graph. ( 2, 5 6 )In Problems 11-18, match each point in polar coordinates with either A,B,C,orD on the graph. ( 2, 5 6 )In Problems 11-18, match each point in polar coordinates with either A,B,C,orD on the graph. ( 2, 7 6 )In Problems 11-18, match each point in polar coordinates with either A,B,C,orD on the graph. ( 2, 11 6 )In Problems 19-32, plot each point given in polar coordinates. (3, 90 )In Problems 19-32, plot each point given in polar coordinates. (4, 270 )In Problems 19-32, plot each point given in polar coordinates. (2,0)In Problems 19-32, plot each point given in polar coordinates. (3,)In Problems 19-32, plot each point given in polar coordinates. (6, 6 )