An angle whose measure is 92° is in standard position. In which quadrant does the terminal side of the angle fall?
answer
Quadrant II
question
What are two possible measures of the angle below?
mc009-1.jpg
answer
-270° and 90°
question
An angle whose measure is 40° is in standard position. In which quadrant does the terminal side of the angle fall?
answer
Quadrant I
question
An angle measuring (525n)° is in standard position. For which value of n will the terminal side fall along the negative portion of the y-axis?
answer
Not n = 2
question
Angle x is coterminal with angle y. If the measure of angle x is greater than the measure of angle y, which statement is true regarding the values of x and y?
answer
mc024-3.jpg, for any positive integer n (c)
question
Which angle has a positive measure?
answer
Not mc001-1.jpg (A)
question
An angle measuring (870n)° is in standard position. For which value of n will the terminal side fall along the positive portion of the y-axis?
answer
n=3
question
Angle T has a measure between 0 and 360 and is coterminal with a -710° angle. What is the measure of angle T?
answer
not 15
question
Which expression finds the measure of an angle that is coterminal with a 45° angle?
answer
Not 45° + 180°
question
An angle whose measure is -102° is in standard position. In which quadrant does the terminal side of the angle fall?
answer
Quadrant III
question
Which angle has a positive measure?
answer
Not mc002-3.jpg (c)
question
Which measure is of an angle that is coterminal with a 425° angle?
answer
Not 425° + (960n)°, for any integer n
Not 425° - (840n)°, for any integer n
question
Which of the following could be the measure of the angle below?
mc008-1.jpg
answer
-180°
question
An angle whose measure is -302° is in standard position. In which quadrant does the terminal side of the angle fall?
answer
Quadrant I
question
What are two possible measures of the angle below?
mc009-1.jpg
answer
-270° and 90°
question
Which expression finds the measure of an angle that is coterminal with a 45° angle?
answer
45° + 360°
question
An angle whose measure is 92° is in standard position. In which quadrant does the terminal side of the angle fall?
answer
Quadrant II
question
Which of the following represents the measures of all angles coterminal with a 418° angle?
answer
58 + 360n, for any integer n
question
An angle measuring (468n)° is in standard position. For which value of n will the terminal side fall along the negative portion of the x-axis?
answer
Not n=4
question
Which expression finds the measure of an angle that is coterminal with a 126° angle?
answer
126° + (720n)°, for any integer n
question
Angle D has a measure between 0 and 360 and is coterminal with a -920° angle. What is the measure of angle D?
answer
160°
question
Which of the following are in the correct order from least to greatest?
Which expression converts mc001-1.jpg radians to degrees?
answer
Not (a) mc001-2.jpg
question
What is 270° converted to radians?
answer
3pi/2
question
Which of the following are in correct order from greatest to least?
answer
Not (c) mc013-9.jpg, mc013-10.jpg, mc013-11.jpg, mc013-12.jpg, 330°
question
What is the approximate length of arc s on the circle below? Use 3.14 for mc024-1.jpg. Round your answer to the nearest tenth.
mc024-2.jpg
answer
6.3 in.
question
What is mc004-1.jpg radians converted to degrees? If necessary, round your answer to the nearest degree.
answer
60
question
An angle that shares the same sine value of an angle that measures mc022-1.jpg radians is located where?
answer
Quadrant IV
question
What is the reference angle for a 240° angle?
answer
60
question
Which of the following explains why cos60 = sin30 using the unit circle?
answer
Not The side opposite a 30° angle is the same as the side adjacent to a 60° angle in a right triangle. On a unit circle, the x (sin) distance of a 30° angle is the same as the y (cos) distance of a 60° angle.
Not The ratios describe different sides of the same right triangle. On a unit circle, the x (sin) distance of a 30° angle is the same as the y (cos) distance of a 60° angle.
question
Which of the following best explains why mc020-1.jpg?
answer
Not The angles do not have the same reference angle or the same sign.
Not The angles do not have the same reference angle.
question
On the unit circle, where mc007-1.jpg, when is mc007-2.jpg undefined?
answer
(c) mc007-6.jpg and mc007-7.jpg
question
Which of the following is true of the values of x and y in the diagram below?
mc010-1.jpg
answer
Not y + x = 1
question
For which value of mc001-1.jpg is mc001-2.jpg?
mc001-3.jpg
answer
(c) mc001-6.jpg
question
The radius of the circle below intersects the unit circle at mc009-1.jpg. What is the approximate value of mc009-2.jpg?
mc009-3.jpg
[Not drawn to scale]
answer
Not 36.9 degrees
Not 1.0 radians
question
Which of the following is true of the location of an angle, mc025-1.jpg, whose tangent value is mc025-2.jpg?
answer
Not mc025-5.jpg has a 60-degree reference angle and is located in Quadrant II or IV
Not mc025-6.jpg has a 60-degree reference angle and is located in Quadrant II or III
question
Which expression is equivalent to mc018-1.jpg?
answer
Not (a) mc018-2.jpg
question
In the diagram below, mc005-1.jpg = mc005-2.jpg. What is the value of m?
mc005-3.jpg
answer
Not (c) mc005-6.jpg
Not (a) mc005-4.jpg
question
The terminal side of an angle measuring mc006-1.jpg radians intersects the unit circle at what point?
answer
Not (b) mc006-3.jpg
Not (c) mc006-4.jpg
question
What is the value of mc003-1.jpg in the diagram below?
mc003-2.jpg
answer
Not 7/25
question
Which of the following best explains why mc021-1.jpg?
answer
Not The angles do not have the same reference angle or the same sign.
question
What are the values of m and mc012-1.jpg in the diagram below?
mc012-2.jpg
answer
Not (b) mc012-5.jpg, mc012-6.jpg
question
On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance from the y-axis to the same point. What is sinmc013-1.jpg?
mc013-2.jpg
answer
Not 0.2
question
What is the value of mc004-1.jpg in the unit circle below?
mc004-2.jpg
answer
Not 1/2
Not mc004-5.jpg (c)
question
Which of the following best explains why mc021-1.jpg?
answer
Not Tangent is positive in the second quadrant and negative in the fourth quadrant.
question
What are the values of m and mc012-1.jpg in the diagram below?
mc012-2.jpg
answer
Not (d) mc012-9.jpg, mc012-10.jpg
question
The angle measures associated with which set of ordered pairs share the same reference angle?
answer
(c) mc023-3.jpg
question
Which of the following is true of the location of the terminal side of an angle, mc024-1.jpg, whose sine value is mc024-2.jpg?
answer
mc024-3.jpg has a reference angle of 30° and is in Quadrant I or II
question
On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance from the y-axis to the same point. What is sinmc013-1.jpg?
mc013-2.jpg
answer
Not mc013-3.jpg (a)
question
Which values for mc017-1.jpg have the same reference angles?
answer
Not mc017-2.jpg, mc017-3.jpg, mc017-4.jpg (a)
question
What is the simplest form of the expression below?
mc016-1.jpg
answer
Not csc mc016-4.jpg
question
For which value of mc019-1.jpg is cot (mc019-2.jpg) undefined?
answer
Not 270
question
If cot mc007-1.jpg = mc007-2.jpg, what is the value of csc mc007-3.jpg?
answer
(a) mc007-4.jpg
question
Which of the following is a simpler way to write mc011-1.jpg?
answer
cot mc011-5.jpg
question
What is the exact value of cos(-60º)?
answer
1/2
question
Which of the following is a simpler form of the expression mc014-1.jpg?
answer
sec mc014-2.jpg
question
Which results from multiplying the six trigonometric functions?
answer
Not -1
question
Which function is undefined when mc018-1.jpg radians?
answer
tan mc018-5.jpg
question
What is the value of csc A in the triangle below?
mc004-1.jpg
answer
Not 9/16
question
Which equation finds the value of x in the triangle below?
mc006-1.jpg
answer
Not (b) mc006-3.jpg
question
What are the exact values of the six trigonometric functions for mc026-1.jpg radians?
answer
(c) mc026-4.jpg
question
Which solution finds the value of x in the triangle below?
mc005-1.jpg
answer
Not (b) mc005-3.jpg
question
Which of the following is cot(mc013-1.jpg) sec(mc013-2.jpg) in simplified form?
answer
Not tan mc013-4.jpg
question
What is the exact value of mc024-1.jpg?
answer
Not (b) mc024-3.jpg
question
If tan mc002-1.jpg = mc002-2.jpg, what is the value of cot mc002-3.jpg?
answer
60/11
question
Consider the relationship below, given mc012-1.jpg.
mc012-2.jpg
Which of the following best explains how this relationship and the value of sin mc012-3.jpg can be used to find the other trigonometric values?
answer
The values of sin mc012-4.jpg and cos mc012-5.jpg represent the legs of a right triangle with a hypotenuse of 1; therefore, solving for cos mc012-6.jpg finds the unknown leg, and then all other trigonometric values can be found.
question
Based on Pythagorean identities, which equation is true?
answer
Not (c) mc002-3.jpg
question
Given that mc005-1.jpg, what is the value of mc005-2.jpg?
answer
Not (a) mc005-3.jpg
question
Given that mc006-1.jpg, what is the value of mc006-2.jpg, for mc006-3.jpg?
answer
20/29
question
Keisha and David each found the same value for mc011-1.jpg, as shown below, given mc011-2.jpg.
Keisha's Solution
David's Solution
mc011-3.jpg
mc011-4.jpg
answer
Not Keisha's procedure is correct.
question
The terminal side of an angle in standard position passes through P(15, -8). What is the value of mc018-1.jpg?
answer
Not (d) mc018-5.jpg
question
A student uses the equation mc013-1.jpg to represent the speed, s, in feet per second, of a toy car driving around a circular track having an angle of incline mc013-2.jpg, where mc013-3.jpg. To solve the problem, the student used the given value of mc013-4.jpg to find the value of mc013-5.jpg and then substituted the value of mc013-6.jpg in the equation above to solve for s. What is the approximate value of s, the speed of the car in feet per second?
answer
5.3
question
Which Pythagorean identity is correct?
answer
Not (d) mc001-4.jpg
question
The terminal side of an angle in standard position passes through P(-3, -4). What is the value of mc017-1.jpg?
answer
Not (b) mc017-3.jpg
not (c) mc017-4.jpg
question
A student uses the equation mc013-1.jpg to represent the speed, s, in feet per second, of a toy car driving around a circular track having an angle of incline mc013-2.jpg, where mc013-3.jpg. To solve the problem, the student used the given value of mc013-4.jpg to find the value of mc013-5.jpg and then substituted the value of mc013-6.jpg in the equation above to solve for s. What is the approximate value of s, the speed of the car in feet per second?
answer
5.3
question
If mc008-1.jpg, which of the following represents approximate values of mc008-2.jpg and mc008-3.jpg, for mc008-4.jpg?
answer
Not (c)
mc008-7.jpg
question
Three trigonometric functions for a given angle are shown below.
mc023-1.jpg
What are the coordinates of point (x, y) on the terminal ray of angle mc023-2.jpg, assuming that the values above were not simplified?
answer
Not (5,-12)
question
The point P(x, y) lies on the terminal side of an angle mc015-1.jpg = mc015-2.jpg in standard position. What are the signs of the values of x and y?
answer
Not x is positive, and y is negative.
question
The point mc021-1.jpg is the point at which the terminal ray of angle mc021-2.jpg intersects the unit circle. What are the values for the cosine and cotangent functions for angle mc021-3.jpg?
answer
(a) mc021-4.jpg
question
The terminal side of an angle in standard position passes through P(15, -8). What is the value of mc018-1.jpg?
answer
Not (a) mc018-2.jpg
question
Given that mc010-1.jpg, what is the value of mc010-2.jpg, for mc010-3.jpg?
answer
sqrt 2
question
If mc008-1.jpg, which equation represents mc008-2.jpg?
answer
B mc008-4.jpg
question
Fatima wants to find the value of mc004-1.jpg, given mc004-2.jpg. Which identity would be best for Fatima to use?
answer
D mc004-6.jpg
question
Haruto simplified the value below.
mc025-1.jpg
Which statement explains whether Haruto is correct?
answer
Haruto is correct because the angle is coterminal with mc025-2.jpg and the reference angle is mc025-3.jpg.
question
Which of the following best explains the value of mc008-1.jpg on the unit circle below?
mc008-2.jpg
answer
mc008-3.jpg mc008-4.jpgmc008-5.jpg mc008-6.jpg mc008-7.jpg
The length opposite the angle is the vertical distance from the x-axis on the graph.
question
Henry is asked to find the exact value of mc026-1.jpg. His steps are shown below.
1. Subtract mc026-2.jpg from mc026-3.jpg as many times as possible:
mc026-4.jpg - mc026-5.jpg = mc026-6.jpg
2. Find the reference angle for mc026-7.jpg: mc026-8.jpg - mc026-9.jpg= mc026-10.jpg.
3. The cosine value for mc026-11.jpg is mc026-12.jpg.
4. The cosine value is positive because mc026-13.jpg is in the first quadrant.
Which of the following describes Henry's errors?
answer
The reference angle should be mc026-14.jpg, and the sign of the value should be negative.
question
Which equation can be used to determine the reference angle, r, if mc016-1.jpg?
answer
B mc016-3.jpg
question
What is the approximate length of arc s on the circle below? Use 3.14 for mc025-1.jpg. Round your answer to the nearest tenth.
mc025-2.jpg
answer
14.1
question
Which of the following represents the measures of all angles coterminal with a -220° angle?
answer
140 + 360n, for any integer n
question
A student is given that point P(a, b) lies on the terminal ray of angle mc026-1.jpg, which is between mc026-2.jpg radians and 2mc026-3.jpg radians. The student uses the steps below to find cos mc026-4.jpg.
Step 1 Find the quadrant in which P(a, b) lies:
P(a, b) is in Quadrant IV.
Step 2 Use the point and the Pythagorean theorem to determine the value of r:
mc026-5.jpg, but since r must be positive, mc026-6.jpg.
Step 3 Determine cos mc026-7.jpg.
mc026-8.jpg, where a and b are positive.
Which of the following explains whether the student is correct?
answer
A The student made an error in step 3 because a is positive in Quadrant IV; therefore, mc026-9.jpg.
question
Which expression converts 8 radians to degrees?
answer
D mc003-4.jpg
question
If mc003-1.jpg , what is the approximate value of csc mc003-2.jpg?
answer
3.2362
question
What is 720° converted to radians?
answer
4 pi
question
Angle B has a measure between 0 and 360 and is coterminal with a -865° angle. What is the measure of angle B?
answer
215
question
What is the value of mc019-1.jpg given the diagram below?
mc019-2.jpg
answer
A mc019-3.jpg
question
Which angle is in standard position?
answer
C mc003-3.jpg
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