Math 1022 Exam 3
(CHAPTER 10.1) If a>0, then which of the following ordered pairs given in polar coordinates describes a point that lies on the negative y-axis of a rectangular coordinate system? a. (a,−π/2) b. (−a,3π/2) c. (a,−3π/2) d. (a,π/2)
a. (a,−π/2)
(CHAPTER 10.1) Which of the following statements is not a valid strategy when converting an equation from polar form to rectangular form? a. Multiply both sides of the polar equation by r^2 then substitute sin2θ+cos2θ for r^2 b. Square both sides of the polar equation c. Rewrite the polar equation in a form that involves the expression tanθ then substitute y/x for tanθ d. Multiply both sides of the polar equation by r
a. Multiply both sides of the polar equation by r^2 then substitute sin2θ+cos2θ for r^2
(CHAPTER 8.5) Which of the following is not a valid strategy for solving the given equation? a. To solve the equation cos2θ=sinθcosθ, first divide both sides by cosθ b. To solve the equation cos2θ=sinθcosθ, first subtract sinθcosθ from both sides, then factor out the common factor of cosθ on the left side c. To solve sin2θ+2cosθsin2θ=0, first factor out the common factor of sin2θ on the left side d. To solve the equation cos2θ=1, first take the square root of both sides
a. To solve the equation cos2θ=sinθcosθ, first divide both sides by cosθ
(CHAPTER 10.1) Which of the following ordered pairs does not describe the given point in a polar coordinate system? a. (3,π/4) b. (−3,7π/4) c. (−3,5π/4) d. (-3,3π/4)
b. (−3,7π/4)
(CHAPTER 10.1) Which of the following statements is not a valid strategy when converting an equation from rectangular form to polar form? a. Replace x with rc the form x+y with sqrt rcosθ b. Replace expressions of the form x+y with sqrt r c. Replace x^2+y^2 with r^2 d. Replace y with rsinθ
b. Replace expressions of the form x+y with sqrt r
(CHAPTER 10.2) Which of the following statements best describes the graph of r2=a2cos2θ? a. The graph is a lemniscate. The endpoints of the two loops of the lemniscate occur when θ=π/3 and θ=4π/3 b. The graph is a lemniscate. The endpoints of the two loops of the lemniscate occur when θ=0 andθ =π c. The graph is a lemniscate. The endpoints of the two loops of the lemniscate occur when θ=π/4 and θ=5π/4 d. The graph is a lemniscate. The endpoints of the two loops of the lemniscate occur when θ=π/2 and θ=3π/2
b. The graph is a lemniscate. The endpoints of the two loops of the lemniscate occur when θ=0 andθ =π
(CHAPTER 10.2) If a<0and b<a, then which of the following statements best describes the graph of r=a+bsinθ? a. The graph is a limacon with a dimple b. The graph is a limacon with an inner loop c. The graph is a cardioid d. The graph is a limacon with no inner loop and no dimple
b. The graph is a limacon with an inner loop
(CHAPTER 10.2) If a≠0, then which of the following polar equations is represented by the graph of a circle whose center does not lie along the line? a. r=a b. r=-asinθ c. r=acosθ d. r=-a
b. r=-asinθ
(CHAPTER 10.2) Which of the following polar equations is represented by the graph of a horizontal line for a>0, b>0, and c>0? a. r=a b. rsinθ=a c. arcosθ+brsinθ=c d. rcosθ
b. rsinθ=a
(CHAPTER 8.5) Which of the following is not a trigonometric equation that is linear in form? a. sqrt 3 tanθ+1=0 b. sinθ cosθ=-1/2 c. tan(θ+π/6)+1=0 θ+π/6 d. sinθ/2=-sqrt 3/2
b. sinθ cosθ=-1/2
(CHAPTER 8.3) If a/2 is an angle with a terminal side lying in Quad III, then which of the following expressions is equivalent to sin (a/2)? a. sqrt 1+cos a/2 b. sqrt 1-cos a/2 c. - sqrt 1- cos a/2 d. - sqrt 1+ cos a/2
c. -sqrt 1-cos a/2
(CHAPTER 8.5) Which of the following statements is true? a. It is not possible for a trigonometric equation to have infinitely many solutions. b. Every trigonometric equation has at least one solution on the interval [0, 2π) c. It is possible for a trigonometric equation to have general solutions but not have a solution on the interval [0, 2π) d. Every trigonometric equation has at least two distinct solutions on the interval [0, 2π)
c. It is possible for a trigonometric equation to have general solutions but not have a solution on the interval [0, 2π)
(CHAPTER 8.3) If a/2 is an angle with a terminal side lying in Quad IV, then which of the following expressions is NOT equivalent to tan (a/2)? a. 1 - cos a/ sin a b. - sqrt 1- cos a/ 1+ cos a c. sqrt 1- cos a/ 1+ cos a d. sin a/ 1 + cos a
c. sqrt 1-cos a/1+cos a
(CHAPTER 10.1) If a>0,then which of the following ordered pairs given in rectangular coordinates corresponds to the ordered pair (a,π) in polar coordinates? a. (0,-a) b. (a,0) c. (0,a) d. (-a,0)
d. (-a,0)
(CHAPTER 10.2) If a≠0 and if n is an integer, then which of the following statements is not true? a. The graph of r=asinθ is a rose with n petals if n is odd b. The graph of r=acosθ is a rose with at least one petal having an endpoint lying along the line θ=0 if n is even c. The graph of r=acosθ is a rose with n petals if n is odd d. The graph of r=asinθ is a rose with at least one petal having an endpoint lying along the line θ=0 if n is even
d. The graph of r=asinθ is a rose with at least one petal having an endpoint lying along the line θ=0 if n is even
