Pre Calc Concept Questions

Describe the horizontal and vertical shift of the function y = 5sin(4(theta) - pi) + 1 a) 1 unit up, (pi/4) units right b) 1 unit up, (pi/4) units left c) 1 unit up, pi units right d) 1 unit down, (pi/4) units right

a) 1 unit up, (pi/4) units right

What ratio is used to convert between radians and degres? a) 180/(pi) b) 360/(pi) c) (pi)/90 d) 7(pi)/2

a) 180/(pi)

Although there are many anlges that satisfy the equation, sin(theta) = 1/2, why do we say there is a single solution? a) Solving the equation utilizes the arcisne function, which restricts the range to a single answer. b) The sine function is periodic c) The range fo the sine fucntion is IyI less than or equal to 1 d) The domain of the sin function is all real numbers

a) Solving the equation utilizes the arcsine function, which restricts the range to a single answer

How can trig functions have inverses even though none of them pass the horizontal line test? a) We restrict the domain of the trig function, thus allowing an inverse to exist b) we restrict the range of the trig function, thus allowing an inverse to exist c) Trig functions never have an inverse d) The inverse exists but not as a function.

a) We restrict the domain of the trig function, thus allowing an inverse to exist

Which expression equals tan23^O? a) cot 23^O b) tan 67^O c) cot 67^O d) tan 46^O

a) cot 23^O

The standard period for the tangent and cotangent functions is: a) 1 b) (pi) c) 2(pi) d) (pi) + 1

b) (pi)

What must be true for the equation for sector area, A = (theta/2)*r^2 a) (Theta) must be in degrees b) (Theta) must be in radians c) r must be measured in centimeters d) the equation is never true.

b) (theta) must be in radians

The value of csc^-1 2 equals a) arcsin 2 b) arcsin 1/2 c) arccos 2 d) arccos 1/2

b) arcsin 1/2

Which statement is NOT true? a) arcsin(sin 5(pi)/6) = 5(pi)/6 b) arccos(cos 5(pi)/6) = 5(pi)/6 c) arctan(tan - (pi)/6) = -(pi)/6 d) arccos(cos 7(pi)/6) = 5(pi)/6

c) arctan(tan - (pi)/6) = -(pi)/6

For which of the following will the unit circle NOT help us fin the exact value of tan 75^O a) tan(120-45) b) tan(45+30) c) tan(150/2) d) tan(90-15)

d) tan(90-15)

Which of the following does NOT come from the identity sin^2(theta) + cos^2(theta) = 1? a) sin^2(theta) = 1 - cos^2(theta) b) 1 + cot ^2(theta) = csc^2(theta) c) cos^2(theta) = sin^2(theta) + 1 d) tan^2(theta) + 1 = sec^2(theta)

a) sin^2(theta) = 1 - cos^2(theta)

Which equation is equal to the equation, y = -sin(theta) a) y = sin -(theta) b) y = cos(theta) c) y = cos - (theta) d) y = -cos(theta)

a) y = sin -(theta)

If (theta) is not in the range of inverse sine function and sin(theta) is negative, what is the solution to arcsin(sin(theta))? a) (theta) b) the reference angle for (theta) c) the negative of the reference angle for (theta) d) 180 or (or (pi)) minus the reference angle for (theta)

c) the negative of the reference angle for (theta)

The value of trig functions is determined by an angle and: a) 1 - 2 - (sqrt 5) b) 1 - 1 - (sqrt 2) c) 3 - 4 - 5 d) 1 - (sqrt 3) - 2

d) 1 - (sqrt 3) - 2

Which is NOT helpful in solving a trig identity problem? a) Change all the terms on one side to sine and cosine functions b) Choose the most complicated side of the equatin to manipulate c) Be aware of opportunities to use the Pythagorean identites d) Cry like a baby

d) Cry like a baby

Which is NOT helpful in solving a trig identity problem. a) Change all the terms on one side to sine and cosine function b) Choose the most complicated side of the equation to manipulate. c) Be aware of opportunitie to use the known trig identities d) Hoping the problem goes away on its own.

d) Hoping the problem goes away on its own.

Which triangle scenario requires the asinb test for the number of solutions given the right data? a) ASA b) SSS c) SAA d) SSA

d) SSA

Which is the best technique for solving a quadrativ trig equation? a) Use the appropriate inverse trig function immediately b) Write everything in terms of sine and cosine c) Give u d) Use substitution to write the equation as a polynomial and factor

d) Use substitution to write the equation as a polynomial and factor

The graphs of the sine and cosine functions look like: a) a V b) a staricase c) a straight line d) a wave

d) a wave

Which correctly describes the input-output of trig functions? a) angle-angle b) number-number c) number-angle d) angle-number

d) angle-number

What term identifies the condition where two functions equal each other whenever they are defined? a) inverse b) reflexive c) commutative d) identity

d) identity

Which correctly describes the input-output of inverse trig functions? a) angle-angle b) number-number c) angle-number d) number-angle

d) number-angle

Why can't you use the Law of Sines to solve the triangle with the following information given? a=34 b=27 c=50^O a) the sine may be 0 for one of the angles b) the Law of Sines requires knowing a side and the angle opposite c) the third side may have length 0 d) you can use the Law of Sines

d) you can use the Law of Sines

How can trig functions have inverses even though none of them pass the horizontal line test? a) The inverse exists but not as a function. b) We restrict the domain of the trig function, thus allowing an inverse to exist c) We restrict the range of the trig function, thus allowing an inverse to exist d) Trig functions never have an inverse.

b) We restrict the domain of the trig function, thus allowing an inverse to exist

Which statement is NOT true? a) arccos(cos 7(pi)/6) = 5(pi)/6 b) arcsin(sin 5(pi)/6) = 5(pi)/6 c) arccos(cos 5(pi)/6) = 5(pi)/6 d) arctan(tan - (pi)/6) = -(pi)/6

b) arcsin(sin 5(pi)/6) = 5(pi)/6

Which expression is always equal to the expression sin(theta) if (theta) is in quadrant 1? a) sin(90^O - (theta)) b) cos(90^O - (theta)) c) cos(theta) d) cos 2(theta)

b) cos(90^O - (theta))

How does the law of cosisnes reconcile with the Pythagorean Theorem> a) sin 90^O = 0 b) cos90^O = 0 c) sin90^O = 1 d) cos90^O = 1

b) cos90^O = 0

The functions sin(theta) and arcsin x are called: a) identity functions b) inverse functions c) compatible functions d) friendly functions

b) inverse functions

Why does the Law of Cosines always work to fin the measrue of an angle of triangle? a) cosines are more powerful than sines b) the range of the arccosine function is [0,180] c) it only works on right traignles d) the cosine function is the complementary function to the sine function

b) the range of the arccosine function is [0,180]

Which of the following equations is identical to the equation, cot(2(theta)/5) = - 1/(sqrt 3) a) tan 5/2(theta) = - 1/(sqrt 3) b) tan 2(theta)/5 = - 1/(sqrt 3) c) tan 2(theta)/5 = - (sqrt 3)/1 d) tan 5/2(theta) = - (sqrt 3)/1

c) tan 2(theta)/5 = - (sqrt 3)/1

Given b = 12, c = 7, and B = 50^O, which can NOT be eliminated immediately as a possible length for a? a) 6 b) 9 c) 15 d) 20

c) 15

How many solutions would we expect to be on the unit circle for equation sin^2(theta) = 1/2 a) 0 b) 2 c) 4 d) impossible to guess

c) 4

Two gears on a bike are connected by a chain. The larger gear has a radius of 5 inches and the smaller gear has a radius of 1 inch. If the larger gear is revolving at a rate of 180 revolutions per minutes, at what speed is the smaller gear revolving in revolutions per minute? a) 36 b) 180 c) 900 d) 1800

c) 900

Which is the best reason to write complex numbers using trig functions? a) Because it is fun c) Because multiplying complex numbers in trig form is easier c) Because adding complex numbers in trig form is easier d) Because the conjugate pairs in complex solution are accounted for in the wave like graph of the sine.

c) Because multiplying complex numbers in trig form is easier

When solvin a triangle problem with 2 solutions, why is the defualt solution an acute angle? a) It is not default, we choose the acute angle b) Acute angles are better than obtuse angles c) The arcsine function forces us to find the acute angle d) It is easier to find the acute angle than the obtuse angle

c) The arcsine function forces us to find the acute angle

Which of the following quantities always equals 1? a) cos^2(theta) - sin^2(theta) b) -cos^2 - sin^2(theta) c) cos^2(theta) + sin^2(theta) d) -cos^2(theta) + sin^2(theta)

c) cos^2(theta) + sin^2(theta)

You are given the following information about a triangle: a = 12 b = 25 c = 31. Which is the BEST first step to solve the triangle? a) find a using the law of cosines b) find b using the law of sines c) find c using the law of cosines d) there is no best first step

c) find c using the law of cosines

Why is using the equation, A = 1/2absinc, easy for a right triangle? a) sin90^O = 0 b) cos90^O = 1 c) sin 90^O = 1 d) It isn't any easier than other triangles

c) sin 90^O = 1