Math 1022 Multiple Choice
U2 7.2b: If A, B, and C are constants, then which of the following is true about the graph of y=A cos (Bx-C) + D?
The range is [-|A|+D, |A|+D]
U1 6.4: Which of the following is not a cofunction identity?
sec θ = cos(π/2-θ)
U1 6.5: Which of the following angles does not belong to the π/4 family of angles.
θ = 10π/4
U3 8.3: If α/2 is an angle with a terminal side lying in Quadrant III, then which of the following expressions is equivalent to sin α/2?
√(1 - cos (α) / 2)
U3 8.5: Which of the following is not a trigonometric equation that is linear in form?
sinθcosθ=-1/2
U3 8.1: Which of the following is not a variation of a Pythagorean Identity?
1−cot²θ=csc²θ
U1 6.5: Which of the following statements is true?
If θ is an angle belonging to π/6, π/3, π/4 families, then the reference angle will be π/6, π/3, π/4, respectively.
U4 9.4: Which of the following statements is true about finding the area of a triangle given that A, B, and C are the measures of the angles, a, b, and c are the lengths of the sides opposite the corresponding angles, and h is the length of an altitude?
In order to find the area of any triangle, the lengths of any two sides and the measure of any angle, the measure of any two angles and the length of one side, or the lengths of three sides of a triangle must be known.
U4 9.1: When solving a right triangle, if the lengths of all three sides of the triangle are known, then which acute angle must be determined first?
It does not matter which angle to determine first.
U3 8.5: Which of the following statements is true?
It is possible for a trigonometric equation to have general solutions but not have a solution on the interval [0, 2π)
U4 9.3: If A, B, and C are the measures of the angles of any triangle and if a, b, and c are the lengths of the sides opposite the corresponding angles, then which of the following is a form of the Law of Cosines?
b²=a²+c²-2ac cosB
U2 7.4: What is the range of y=tan⁻¹(x)
(-π /2, π /2)
U4 9.2: Which of the following statements best describes an oblique triangle?
An oblique triangle cannot have a right angle
U4 10.1: Which of the following statements is not a valid strategy when converting an equation from polar form to rectangular form?
Multiply both sides of the polar equation by r² then substitute sin²θ+cos²θ for r²
U1 6.3: Which of the following statements is true?
The length of the leg opposite the π/3 angle of a special π/6, π/3, π/2 right triangle is equal to the square root of 3 times the length of the leg opposite the π/6 angle.
U4 9.1: Which two given pieces of information are not helpful when trying to solve a right triangle?
The measure of two acute angles
U2 7.1: Which of the following is not a characteristic of the sine function?
The sine function obtains a relative maximum at x= π /2+πn where n is an integer
U4 9.3: Which of the following phrases best describes the Law of Cosines?
The square of any side of a triangle is equal to the sum of the squares of the remaining two sides, minus twice the product of the two remaining sides and the cosine of the angle between them.
U2 7.3: When sketching the graph of y=A tan(Bx+C)+D which of the following best describe how to determine the x-coordinates of the halfway points of the principle cycle?
The x-coordinate of each halfway point is located halfway between the x-coordinate of the center point and a vertical asymptotes
U2 7.4: What is the domain of the restricted cosine function whose inverse function is y= cos⁻¹(x)
[0, π ]
U1 6.5: For any θ whose terminal side lies in Quadrant IV, which of the following trigonometric expressions is positive?
cos θ sec θ
U1 6.4: Which of the following is not a fundamental identity?
cos θ = tanθ/sinθ
U4 9.3: If A, B, and C are the measures of the angles of any triangle and if a, b, and c are the lengths of the sides opposite the corresponding angles, then which of the following is an alternate form of the Law of Cosines?
cosA=b²+c²-a²/2bc
U1 6.6: For any real number t, if P(x,y) is a point on the unit circle corresponding to t, then which of the following does not accurately define a trigonometric function?
cot t = y/x, x=/=0
U3 8.1: Which of the following is not a valid property of trigonometric functions?
cot(−θ)=cotθ
U1 6.4: Which of the following is not a valid equation?
csc π/6 = cos π/3
U2 7.4: If θ= tan⁻¹(x), then which of the following statements best describe angle θ
The angle θ is an angle satisfying the inequality -π /2 < θ < π /2 having a terminal side lying in Quadrant I, Quadrant IV, on the positive x-axis, on the positive y-axis, or on the negative y-axis
U4 9.4: Which of the following best describes the semiperimeter of a triangle?
The semiperimeter of a triangle is half the sum of the lengths of the three sides of a triangle.
U4 9.2: If S represents the length of a known side of an oblique triangle and if A represents the measure of a known angle, then which of the following triangles cannot be solved using the Law of Sines?
triangle SAS
U4 9.4: If A, B, and C are the measures of the angles of any triangle and if a, b, and c are the lengths of the sides opposite the corresponding angles, then which of the following expressions does not represent the area of the triangle?
(1/2) ac sinA
U4 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 , -π/2)
U4 9.4: Which of the following statements is not true about finding the area of a triangle?
If the measures of all three angles of a triangle are known, then it is possible to find the area using Heron's Formula.
U2 7.1: Which of the following statements describes the definition of amplitude of a sine or cosine function?
The amplitude is the measure of half the distance between the maximum and minimum values.
U1 6.1: Which of the following statements is not true concerning angle measure?
The angle in standard position formed by rotating the terminal side of angle one complete counterclockwise rotation has a radian measure of π radians.
U4 10.1: Which of the following statements is not a valid strategy when converting an equation from rectangular form to polar form?
Replace expressions of the form x+y with √r.
U4 9.3: If S represents the length of a known side of an oblique triangle and if A represents the measure of a known angle, then for which of the following triangles must the Law of Cosines be used to begin to solve the triangle?
SSS
U2 7.3: Which of the following statements is true?
The function y=cot x has infinitely many vertical asymptotes with equations x=nπ where n is an integer
U4 10.2: If a<0 and b<a, then which of the following statements best describes the graph of r=a+bsinθ?
The graph is a limacon with an inner loop
U2 7.3: Which of the following statements is true?
The x-intercepts of y=tan x are the same as the center points of y=tan x
U1 6.6: Which of the following statements is not true?
There are infinitely many points that lie on the graph of the unit circle that have integer coordinates.
U2 7.1: Which of the following is not a characteristic of the cosine function?
The y-intercept is 0
U4 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 θ=0?
r = -a sinθ
U4 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?
r sinθ = a
U4 9.1: In the right triangle provided to the right, suppose that the lengths of sides a and c are known. Also, suppose that the measures of angle A and angle B are known. Which of the following equations cannot be used to determine the length of side b?
tan A= b/a
U1 6.5: If the terminal side of an angle θ lies in Quadrant III, then which of the following is true?
tan θ > 0, sec θ < 0
U2 7.2a: If A, B, and C are constants such that B>1, then which of the following statements is true about the graph of y=A cos (Bx-C)
the period is 2π/B and the phase shift is C/B
U1 6.1: Which of the following statements is not true concerning radian measure?
An angle in standard position having a radian measure of θ = -11π/6 has a terminal side that lies in Quadrant IV.
U1 6.1: Which of the following statements best describes an angle that is in standard position?
An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive x-axis.
U2 7.2b: When sketching functions of the form y=Asin(Bx−C)+D and y=Acos(Bx−C)+D, which of the following statements is true?
An interval for one complete cycle of the graph is [C/B , C/B + P] where P is the period of the given function.
U4 10.1: Which of the following ordered pairs does not describe the given point in a polar coordinate system?
(-3 , 7π/4)
U4 10.1:If a>0, then which of the following ordered pairs given in rectangular coordinates corresponds to the ordered pair left parenthesis a comma pi right parenthesis(a,π) in polar coordinates
(-a , 0)
U1 6.1: Which of the following statements best describes two coterminal angles?
Two angles in standard position are coterminal if they have the same terminal side.
U1 6.4: Which of the following is not a fundamental identity?
sec² + 1 = tan²θ
U3 8.3: If α/2 is an angle with a terminal side lying in Quadrant IV, then which of the following expressions is not equivalent to tan α/2?
√(1 - cos α / 1 + cos α)
U4 9.4: Suppose that a triangle has side lengths of a, b, and c and suppose that s is the semiperimeter of the triangle. Then which of the following expressions describes the area of the triangle?
√s(s-a)(s-b)(s-c)
U2 7.1: Which of the following statements is not true about the function y= A cos (Bx)
If B>0, then the function y=A cos (-Bx) is equivalent to the function y= - A cos (Bx)
U3 8.1: Which of the following is not a process commonly used to verify an identity?
If more than one term appears in the denominator of an expression, try using long division to simplify the expression.
U1 6.2: Which of the following statements is not true? Choose the correct answer below.
If the central angle of a sector of a circle is θ=5 degrees and the redius of the circle is r=2 cm, then the arc length of the sector of the circle is 10 cm.
U1 6.3: Which of the following statements is not true?
Similar triangles have the same shape and size
U2 7.4: If θ=sin⁻¹(x), then which of the following statements best describes angle θ?
The angle θ is an angle satisfying the inequality -π /2 ≤ θ ≤ π /2 having a terminal side lying in Quadrant I, Quadrant IV, on the positive x-axis, on the positive y-axis, or on the negative y-axis
U2 7.4: If θ = cos⁻¹(x), then which of the following statements describes angle θ
The angle θ is an angle satisfying the inequality 0≤ θ ≤ π having a terminal side lying in Quadrant I, Quadrant II, on the positive x-axis, on the positive y-axis, or on the negative x-axis
U4 10.2: Which of the following statements best describes the graph of r²=a²cos2θ
The graph is a lemniscate. The endpoints of the two loops of the lemniscate occur when θ=0 and θ=π
U4 10.2: If a≠0 and if n is an integer, then which of the following statements is not true?
The graph of r=a sin n(θ) is a rose with at least one petal having an endpoint lying along the line (θ)=0 if n is even.
U2 7.3: Which of the following statements is not true?
The graph of y=csc x is symmetric about the y-axis
U2 7.2a: Which of the following statement best describes the graph of y=sin (x+C) where C>0
The graph of y=sin (x+C) can be obtained by horizontally shifting each quarter point of y=sin(x) to the left C units
U1 6.3: Which of the following statements is true?
The length of the leg opposite either of the π/4 angles of a special π/4, π/4, π/2 right triangle with a hypotenuse of SQRT 2 is equal to 1.
U4 9.1: Which of the following statements accurately describes the relationship between the two acute angles of a right triangle?
The two acute angles of a right triangle are always complementary.
U4 9.2: When attempting to solve an oblique triangle given the lengths of two sides and the measure of an angle not included between the two sides, which of the following best describes this case?
This case could result in a solution where there is no triangle, one unique triangle, or two unique triangles.
U1 6.1: Which of the following statements is true concerning the conversion between degree and radian measure?
To convert from radians to degrees, multiply by 180 degrees and divide by π.
U3 8.5: Which of the following is not a valid strategy for solving the given equation?
To solve the equation cos²θ= sinθ cosθ, first divide both sides by cos θ
U1 6.4: Suppose that a right triangle has an acute angle θ and side lengths of hyp, opp, and adj. Which of the following does not accurately define a trigonometric function?
cotθ = opp/adj
U3 8.1: Which of the following is true
A trigonometric identity is valid for all values of the independent variable for which both sides of the identity are defined.
U4 9.3: If S represents the length of a known side of an oblique triangle and if A represents the measure of a known angle, then which of the following triangles cannot be solved using either the Law of Sines or the Law of Cosines?
AAA
U1 6.5: Which of the following statements best describes the term general angles?
General angles are angles that are not restricted in size and can be either positive angles, negative angles, or zero.
U1 6.2: Which of the following statements is not true? Choose the correct answer below.
The area of a sector of a circle if given by the equation A=½θr², where θ is an angle given in degrees.
U2 7.3: Which of the following statements is not true?
The function y=sec x is obtains a local maximum at values of x for which the function y=cos x obtains a local maximum
U4 9.1: Which of the following describes the goal of solving right triangles?
The goal of solving a right triangle is to determine the measure of all angles and the length of all sides
