Math 1022
Which of the following best describes the semi perimeter of a triangle?
The semiperimeter of a triangle is half the sum of the lengths of the 3 sides of a triangle.
Given a nonzero vector v=ai+bj, the unit vector in the same direction as v is given by which of the following expressions?
v/IIvII
If the terminal side of an angle theta lies in Quadrant III, then which of the following is true?
tan theta > 0, sec theta < 0
If x/2 is an angle with a terminal side lying in QIII, then which of the following expressions is, equivalent to sin (x/2)?
-the square root of 1- cos x/2
Which of the following is the correct sum formula for the cosine function?
cos (x+b) - cos xcosb-sinxsinb
Which of the following is not a valid double-angle formula for cosine?
cos2theta = 2sin^2 theta-1
If a does not equal 0, then which of the following polar equations is represented by the graph of a circle whose center does not lie along the line theta=0?
r=-asintheta
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 the square root of r
Which of the following expressions does not result in an angle having a terminal side that lies in Quadrant I?
sin ^-1(sin 6pi/5)
Which of the following is not a trigonometric equation that is linear in form?
sin theta cos theta = -1/2
Which of the following can best be evaluated using the half-angle formula for the sine function?
sing (1/2 cos^-1(-2/3))
Which of the following is the correct sum formula for the tangent function?
tan (x+b) = tan x+tanb/1-tanxtanb
Which of the following is the correct difference formula for the tangent function?
tan (x-b) = tan x- tan b/1+tanxtanb
In the right triangle provided, suppose that the lengths of sides a and c are known and that the measures of <A and <B are known. Which of the following equations cannot be used to determine the length of side b?
tan A = b/a
Use the fact the y = sinx is an odd function to determine which of the following expressions is equivalent to -sin(13pi/20).
sin (-13pi/20)
If a>0, then which of the following ordered pairs given in rectangular coordinates corresponds to the ordered pair (a, pi) in polar coordinates?
(-a,0)
What is the rang of y = tan^-1x?
(-pi/2,pi/2)
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 a triangle?
1/2acsinA
Which of the following statements describes a vector that is in standard position?
A vector is in standard position if the initial point coincides with origin
Which of the following statements best describes an oblique triangle?
An oblique triangle cannot have a right angle.
If s represents the length of a known side of an oblique triangle and if the A represents the measure of a known angle, then which of the following trianlges cannot be solved using Law of Sines?
SAS
Which of the following statements describes the definition of amplitude of a sine or cosine function?
The amplitude is the measure of the half the distance between the max and the min values
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 pi radians
If theta = sin ^-1x, then which of the following statements best describes angle theta?
The angle theta is an angle satisfying the inequality -pi/2 less than or equal to theta less than or equal to pi/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
If theta = tan ^-1x, then which of the following statements best describes angle theta?
The angle theta is an angle satisfying the inequality -pi/2 less than theta less than pi/2 having a terminal side lying in Quadrant IV, or on the positive x-axis.
Which of the following statements is not true? Choose the correct answer below
The area of a sector of a circle is given by the equation A=1/2thetar^2, where theta is an angle given in degrees
When sketching the graph y = Atan(Bx+C)+D which of the following best describes how to determine the x-coordinates of the halfway points of the principal cycle?
The x-coordinate of each halfway point is located halfway between the x-coordinate of the center point and a vertical asymptote.
Which of the following statements is true?
The x-intercepts of y = tanx are the same as the x-coordinates of the center points of y = tanx
Given the expression csc (cos ^-1(-1/2), which of the following is not true?
The expression csc (cos^-1(-1/2)) is equal to -2/square root of 3
Which of the following statements is not true?
The function of y = sec x obtains a local maximum at values of x for which the function y = cos x obtains a local maximum
Which of the following statements is true?
The function y = cot x has infinitely many vertical asymptotes with equations x = npi where n is an integer.
Which of the following is not a characteristic of the cosine function?
The y-intercept is 0
If -1<b<0, then which of the following statements best describes the solution to the equation cos theta = b on the interval [0, 2pi)?
There are exactly 2 solutions to the equations cos theta = b on the interval [0, 2i). One solution is theta = pi-cos^-1(-b), the other solution is theta = pi + cos^-1(-b)
Which two given pieces of information are not helpful when trying to solve a right triangle?
The measure of two acute angles.
Which of the following is not a characteristic of the sine function?
The sine function obtains a relative maximum at x=pi/2 +pi n where n is an integer.
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 2 sides, minus twice the produce of the 2 remaining sides and the cos of angle between them
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 corrdinates
Which of the following is not a valid strategy for solving the given equation?
To solve the equation cos^2theta=sin theta cos theta, first divide both sides by cos theta
Which of the following statements best describes two coterminal angles?
Two angles in standard position are coterminal if they have the same terminal side
Which of the following statements is true?
Two vectors are equal if they have the same magnitude and same direction
If A, B, & 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?
b^2 = a^2+c^2-2accosB
What is the domain of the restricted cosine function whose inverse function is y = cos ^-1x?
[0,pi]
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 does not equal 0
Suppose that a right triangle has an acute angle theta and side lengths of hyp., opp., and adj. Which of the following does not accurately define a trigonometric function?
cot theta = opp/adj
Which of the following is not a valid equation?
csc pi/6 = cos pi/3
Which of the following describes the goal of solving the right triangles?
The goal of solving a right triangle is to determine the measure of all angles and the length of all sides
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 pi.
Which of the following can best be evaluated using the sum formula for the sine function?
sin [(tan(^-1)1+cos(^-1)the square root of m/2]
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, -pi/2)
If s represents the length of a known side of an oblique triangle, and if the A represents the measure of a known angle, then which of the following triangles cannot be solved using either Law of Sines or Law of Cosines?
AAA
If 3pi/4 less than theta less than 5pi6, then which of the following mathematical statements is true?
cos ^-1 (cos theta) = 0
If a<0 and b<a, then which of the following statements best describes the graph of r=a+bsintheta?
the graph is a limacon with a inner loop
If a does not equal 0 and if n is an integer, then which of the following statements is not true?
the graph of r=asinntheta is a rose with at least one petal having an endpoint lying along the line theta = 0 if n is even
If x/2 is an angle with a terminal side lying in QIV, then which of the following expressions is not equivalent to tan (x/2)?
the square root of 1-cosx/1+ cosx
Which of the following statements is true?
If theta is an angle belonging to the pi/6, pi/3, pi/4 families, then the reference angle will be pi/6, pi/3, pi/4, respectively.
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
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, 2pi).
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 r^2 and then substitute sin^2theta+cos^2theta for h^2.
Which of the following statements best describes the graph of r^2 = a^2cos2theta?
The graph is a lemniscate. The endpoints of the two loops of the lemniscate occur when theta = 0 and theta = pi.
Which of the following statements is not true?
The graph of y = csc x is symmetric about the y-axis
Which of the following statements is true?
The length of the leg opposite either of the pi/4 angles of a special pi/4, pi/4, pi/2 right triangle with a hypotenuse of square root of 2 is equal to 1.
Which of the following statements is true?
The length of the leg opposite the pi/3 angle of a special pi/6, pi/3, pi/2 right triangle is the equal to the square root of 3 times the length of the leg opposite the pi/6 angle.
If A, B, and C are constants such that B>1, then which of the following statements is true about the graph of y=Acos(Bx-C)?
The period is 2pi/B and the phase shift is C/B
Which of the follow statements is not true concerning radian measure?
An angle in standard position having a radian measure of theta=-11pi/6 has a terminal side that lies in Quadrant IV
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
Suppose that a triangle has side lengths of a, b, and c and suppose that s is the semi perimeter of the triangle. Then which of the following expressions describes the area of the triangle?
the square root of s(s-a)(s-b)(s-c)
Which of the following angles does not belong to the pi/4 family of angles?
theta = 10pi/4
If a>0 and b<0, then which of the following describes the direction angle of the vector v=ai+bj?
theta= 2 pi-tan^-1 Ib/aI
Which of the following expressions is equivalent to angle pi/6?
tan ^-1 (tan(-5pi/6))
Use the fact that y = cos x is an even function to determine which of the following expressions is equivalent to -cos (13pi/15)?
-cos(-13pi/15)
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.
Which of the following statements is not true about the function y=Acos(Bx)?
If B>0, then the function y=Acos(Bx) is equivalent to the function y=-Acos(Bx).
Which of the following statements is not true? Choose the correct answer below.
If the central angle of a sector of a circle is theta = 5 degrees and the radius of the circle is r = 2 cm, then the arc length of the sector of the circle is 10 cm.
Which of the following statements is not true about finding the area of a triangle?
If the measure of all 3 angles of a triangle are known, then it is possible to find the area using Heron's formula.
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 2 sides and the measure of an 2 angles and the length of one side, or the lengths of 3 sides of a triangle must be known
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 must the Law of Cosines be used to begin to solve the triangle?
SSS
If theta = cos ^-1x, then which of the following statements best describes angle theta?
The angle theta is an angle satisfying the inequality 0 less than or equal to theta less than or equal to pi 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
Which of the following is not a fundamental identity?
sec^2theta+1 = tan^2 theta
Which of the following is the correct difference formula for the sine function?
sin (x-b) = sinxcosb-cosxsinb
Which of the following statements 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
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
Which of the following statements is true?
The unit circle is symmetric about the x-axis, y-axis, and the origin
When attempting to solve an oblique triangle given the lengths of 2 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.
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 Law of Cosines?
cos A = b^2+c^2-a^2/2bc
Which of the following is not a fundamental identity?
cos theta = tan theta/sin theta
Which of the following polar equations is represented by the graph of a horizontal line for a>0, b>0, and c>0?
rsintheta = a
Which of the following is not a confunction identity?
sec theta = cos (pi/2-theta)