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Unit 6  –  Polar Coordinates and Vectors Vocab

Total questions: 95

Worksheet time: 48mins

Name
Class
Date
1.

What will Unit 6  –  Polar Coordinates and Vectors inform us about? Be specific!

a)
Unit 6 will inform us about polar coordinates, their representation, and operations involving vectors in polar form.
b)
Unit 6 will focus on the history of mathematics.
c)
Unit 6 will cover basic algebra and its applications.
d)
Unit 6 will teach about three-dimensional geometry.
2.

What is polar coordinates?

a)
Polar coordinates are a system for representing points in a plane using a distance and an angle.
b)
A method for calculating distances in three-dimensional space.
c)
A way to represent points using only Cartesian coordinates.
d)
A system that uses only angles to define locations.
3.

What are the two parts of a polar coordinate pair?

a)
The two parts are the diameter (d) and the height (h).
b)
The two parts are the base (b) and the exponent (e).
c)
The two parts are the radius (r) and the angle (θ).
d)
The two parts are the length (l) and the width (w).
4.

When a radius is negative, why does the point flip?

a)
A negative radius has no effect on the point's position.
b)
The point flips because a negative radius reflects the point across the origin.
c)
A negative radius moves the point to a different quadrant without flipping.
d)
The point flips because the radius is squared.
5.

When a angle is negative on a polar coordinate, what direction do you go?

a)
Counterclockwise direction
b)
Diagonal direction
c)
Clockwise direction
d)
Straight up direction
6.

When a angle is positive on a polar coordinate, what direction do you go?

a)
Clockwise
b)
Straight up
c)
Downward
d)
Counterclockwise
7.

What is the equation of find x value of trig function?

a)

rcos(x)=x

b)

rcos(x)=y

8.

What equation to find the y value in polar coordinates?

a)

rsin(x)=y

b)

rsin(x)=x

9.

True or False: One must use triangles to than convert from Polar to Rectangle and Vice Versa

a)
False
b)
Only for Polar to Rectangle
c)
Only for Rectangle to Polar
d)
True
10.

This equation is used to find.... r=x2+y2r=\sqrt[]{x^2+y^2}

a)
the slope of a line in slope-intercept form
b)
the area of a circle with radius r
c)
the perimeter of a rectangle with sides x and y
d)
the distance from the origin to a point (x,y) in Cartesian coordinates
11.

This equation is used to find.... θ=tan⁡−1(yx)\theta=\tan^{-1}\left(\frac{y}{x}\right)

a)
The area of a triangle.
b)
The length of the hypotenuse.
c)
The angle \( \theta \) in a right triangle.
d)
The perimeter of a triangle.
12.

When the radius is negative, the point on a polar cordinate plane must flip over the origin

a)
Yes, the point flips over the origin.
b)
The point moves to a different quadrant.
c)
The point remains unchanged.
d)
The point disappears from the plane.
13.

What are the nine equations of polar equations?

a)
Parabola
b)
Circle, Line, Spiral, Rose curve, Lemniscate, Cardioid, Limacon, Hyperbola, Conic sections.
c)
Quadratic function
d)
Ellipse
14.

What is a circle equation for polar equations?

a)
r = θ
b)
r = 2θ
c)
r = constant
d)
r = sin(θ)
15.

θ=k\theta=k Is a equation for polar coordinates that is.... line

a)
a line at angle k
b)
a spiral with angle k
c)
a parabola opening upwards
d)
a circle with radius k
16.

What is the horizontal equation for polar equations?

a)

rsin⁡(θ)=kr\sin\left(\theta\right)=k

b)
y = r(θ)
c)
x^2 - y^2 = r(θ)
d)
x = r(θ)
17.

What is a vertical equation for polar equations?

a)
r = cos(θ) for a vertical line in polar coordinates.
b)
r = sin(θ) for a vertical line in polar coordinates.
c)
r = θ for a vertical line in polar coordinates.
18.

What is the equation where the polar equation makes a circle with the middle being the origin?

a)
r = 2a
b)
r = a
c)
r = a^2
d)
r = sin(θ)
19.

What is the equation where the polar equation makes a y=mx+b like line?

a)
r = mθ + c
b)
r = aθ + b
c)
r = b + aθ
d)

θ=k\theta=k

20.

What is the equation where the polar equation makes a horizontal line?

a)
r = θ
b)
r = 0
c)
r = a
d)

k = r sin(θ)

21.

What is the equation where the polar equation makes a vertical line?

a)
r = a tan(θ)
b)
r = a sec(θ)
c)
r = a csc(θ)
d)

k = r cos(θ)

22.

What is the equation where the polar equation makes a horizontal movable circle

a)
r = a * cos(θ) + b * sin(θ)
b)

r = a* cos(θ)

c)

r = b * cos(θ)

d)

r = b * sin(θ)

23.

What is the equation where the polar equation makes a vertical movable line?

a)
r = a sin(θ)
b)
r = a sec(θ)
c)
r = a tan(θ)
d)
r = a cos(θ)
24.

What is a cardiod in math?

a)
A cardioid is a type of triangle.
b)
A cardioid is a mathematical function that represents a circle.
c)
A cardioid is a heart-shaped curve in mathematics.
d)
A cardioid is a polygon with four sides.
25.

What is limacon w/out inner loop?

a)
A limacon that is a straight line defined by r = 0.
b)
A limacon with an inner loop defined by r = a - b*cos(θ) or r = a - b*sin(θ) with a < b.
c)
A limacon without an inner loop is a convex polar curve defined by r = a + b*cos(θ) or r = a + b*sin(θ) with a > b.
d)
A limacon defined by r = a + b*cos(θ) or r = a + b*sin(θ) with a = b.
26.

What is limacon w/inner loop?

a)
A limacon with an inner loop is a straight line in polar coordinates.
b)
A limacon with an inner loop is defined by r = a - b * cos(θ) with a > b.
c)
A limacon with an inner loop is a type of ellipse in Cartesian coordinates.
d)
A limacon with an inner loop is a polar curve characterized by the equation r = a + b * cos(θ) or r = a + b * sin(θ) with a < b.
27.

How do you find the radius of r=acos⁡θr=a\cos\theta

a)

∣a2∣\left|\frac{a}{2}\right|

b)

a2\frac{a}{2}

28.

How do you find the center of r=acos⁡θr=a\cos\theta

a)
(a/2, 0)
b)
(a/2, a/2)
c)
(a, 0)
d)
(0, a/2)
29.

True or False: r=acos⁡θr=a\cos\theta is vertical, not horizontal

a)
True
b)
r=a\sin\theta is vertical
c)
It is horizontal
d)
False
30.

True or False: The radius is always positive for consistency sake

a)
The radius can be imaginary
b)
The radius is always zero
c)
True
d)
The radius can be negative in some cases
31.

How do you find the radius of r=asin⁡θr=a\sin\theta

a)

∣a2∣\left|\frac{a}{2}\right|

b)

a2\frac{a}{2}

32.

How do you find the center of r=asin⁡θr=a\sin\theta

a)

(a/2,0)

b)

(0,a/2)

33.

What direction will r=a(1+cos⁡θ)r=a\left(1+\cos\theta\right) go horizontally.

a)
Neither right nor left
b)
Only left
c)
Only right
d)
Both right and left
34.

What direction will r=a(1−cos⁡θ)r=a\left(1-\cos\theta\right) go horizontally.

a)
The direction goes horizontally from right to left.
b)
The direction goes diagonally from bottom left to top right.
c)

The direction goes horizontally from left.

d)
The direction goes vertically from top to bottom.
35.

With what equation can you use to find the diameter of a cardiod?

a)
d = 2a
b)
d = a/2
c)
d = 3a
d)
d = a
36.

Limacon w/out inner loop, a must be compared to b

a)
a must be greater than b
b)
a can be any value compared to b
c)
a must equal b
d)
a must be less than b
37.

r=a+bcos⁡θr=a+b\cos\theta and r=a−bcos⁡θr=a-b\cos\theta give which direction does it have?

a)
The direction is random and not defined.
b)
The direction is symmetric about the polar axis (x-axis).
c)
The direction is circular around the origin.
d)
The direction is vertical along the y-axis.
38.

r=a+bsin⁡θr=a+b\sin\theta and r=a−bsin⁡θr=a-b\sin\theta has a shift in which direction?

a)
No shift, both curves remain unchanged.
b)
Horizontal shift, with both curves shifting to the right.
c)
Vertical shift, with the first curve shifting up and the second curve shifting down.
d)
Diagonal shift, with the first curve shifting up and the second curve shifting down.
39.

Limacon w/out innerloop, how does one find the longest distance and short distance?

a)

Longest distance: a + b; Shortest distance: a - b

b)

Longest distance: a - b; Shortest distance: a + b

40.

With Limacon w/inner loop, what is true about a and b?

a)
a + b = 0
b)
a > b
c)
a < b
d)
a = b
41.

For Limacon w/inner loop, how do you go by finding the long pair?

a)

(a+b)

b)

(b-a)

42.

For Limacon w/inner loop, how do you go by finding the short pair?

a)

(a+b)

b)

(b-a)

43.

What is The Complex Plane compared to the Polar or Rectangular Plane?

a)
The Rectangular Plane uses polar coordinates while the Polar Plane uses Cartesian coordinates.
b)
The Complex Plane is only a one-dimensional representation of complex numbers.
c)
The Complex Plane is a two-dimensional representation of complex numbers, while the Rectangular Plane uses Cartesian coordinates and the Polar Plane uses radius and angle.
d)
The Complex Plane is a three-dimensional representation of real numbers.
44.

Instead of the x axis, what is really on the x-axis for complex plane?

a)
The y-axis.
b)
The real axis.
c)
The imaginary axis.
d)
The z-axis.
45.

Instead of the y axis, what is really on the y-axis for complex plane?

a)
The real part of a complex number.
b)
The modulus of a complex number.
c)
The angle of a complex number.
d)
The imaginary part of a complex number.
46.

What is the template for the complex plane equation?

a)
z = x * yi
b)
z = x + yi
c)
z = x / yi
d)
z = x - yi
47.

True or False: Instead of radius for The Complex Plane, we say maginutde

a)
False
b)
Magnitude is not used in The Complex Plane
c)
Radius is the only term used in mathematics
d)
True
48.

What variable represents the magnitude in the complex plane?

a)
x
b)
y
c)
z
d)
r
49.

How can you convert the complex plane to the polar plane with what equation?

a)
z = r(cos(θ) + i sin(θ)) or z = re^(iθ) where r is the modulus and θ is the argument.
b)
z = r^2e^(iθ)
c)
z = r^2 + iθ
d)
z = r(cos(θ) - i sin(θ))
50.

True or False: When finding all solutions for a trig functions, the function is together, and shouldn't be subtracted on both sides, but instead factored

a)
True
b)
The function can be subtracted on both sides
c)
Factoring is not necessary for solutions
d)
False
51.

Why do we add 180 degrees to tan when the angle isn't in quadrant 1 or 4?

a)
We add 180 degrees to convert to radians.
b)
We add 180 degrees to find the sine value.
c)
We add 180 degrees to simplify the angle.
d)
We add 180 degrees to adjust the angle into the correct quadrant for tangent.
52.

When finding the angle to turn a function from complex to polar, and the angle found with tan is not in Quadrant 1 or 4, what must you add to the angle to fix it?

a)
Add 90 degrees (or π/2 radians) to the angle.
b)
Subtract 180 degrees (or π radians) from the angle.
c)
Add 360 degrees (or 2π radians) to the angle.
d)
Add 180 degrees (or π radians) to the angle.
53.

How do you convert polar plane to complex plane?

a)
z = r * (tan(θ) + i * sec(θ))
b)
z = r * (sin(θ) - i * cos(θ))
c)
z = r * (1 + i * θ)
d)
z = r * (cos(θ) + i * sin(θ)) or z = r * e^(iθ)
54.

What is the De Moivre's Theorme?

a)
De Moivre's Theorem states that all complex numbers are real numbers.
b)
De Moivre's Theorem is used to calculate the area of triangles.
c)
De Moivre's Theorem describes the relationship between logarithms and exponential functions.
d)
De Moivre's Theorem relates complex numbers and trigonometric functions, expressed as (cos(theta) + i*sin(theta))^n = cos(n*theta) + i*sin(n*theta).
55.

True or False: Limacon without a loop, has a less than b,

a)

False

b)

True

56.

What is a vector in precalculus?

a)
A vector is a single point in space.
b)
A vector is a mathematical object with both magnitude and direction.
c)
A vector is a type of polynomial function.
d)
A vector is a scalar quantity with no direction.
57.

What two points are important to understanding vectors?

a)
Position and velocity
b)

initial and terminal

c)
Force and mass
d)
Speed and acceleration
58.

What is magnitude in vectors?

a)
Magnitude is the length of a vector.
b)
Magnitude is the sum of the vector components.
c)
Magnitude is the angle between two vectors.
d)
Magnitude is the direction of a vector.
59.

d=(x2 −x1)+(y2−y1)d=\sqrt[]{\left(x_{2\ }-x_1\right)+\left(y_2-y_1\right)} Is known as the...

a)
Distance formula
b)
Quadratic equation
c)
Slope formula
d)
Pythagorean theorem
60.

Where is the distance formula from?

a)
The distance formula is derived from trigonometry.
b)
The distance formula comes from algebraic equations.
c)
The distance formula is based on calculus.
d)
The distance formula is derived from the Pythagorean theorem.
61.

True or False: The arrow in a vector doesn't say infinity but instead direction

a)
True
b)
The arrow represents magnitude
c)
The arrow indicates speed
d)
The arrow shows distance
62.

What is the notation to write a vector?

a)

∣∣x∣∣ with an arrow∣∣\left|\left|x\right|\left|\ with\ an\ arrow\right|\right|

b)

Literally anything else

63.

True or False: Vectors can't have operations

a)
Vectors have no defined operations
b)
Vectors can only be multiplied
c)
Vectors can only be added
d)
False
64.

When combing vectors graphically, one must connect the initial point of one vector to...

a)
the endpoint of the second vector
b)
the terminal point of the first vector
c)
the midpoint of the first vector
d)
the initial point of the second vector
65.

What is negative vector?

a)
A vector with the same direction as a given vector.
b)
A vector that has no direction or magnitude.
c)
A vector with the opposite direction to a given vector.
d)
A scalar quantity that represents magnitude only.
66.

Negative vectors when combined with other vectors can become an addition of a negative number, rather than a subtract, to find a vector.

a)
Negative vectors can be treated as adding a negative number.
b)
Negative vectors can only be subtracted from other vectors.
c)
Adding a negative vector always results in a positive vector.
d)
Negative vectors have no effect on vector addition.
67.

True or False: Subtracting two vectors is the same as adding by the negative vector after the addition

a)
True
b)
Adding two vectors is the same as subtracting their magnitudes
c)
Subtracting two vectors always results in a positive vector
d)
Subtracting vectors is the same as multiplying by a scalar
68.

What is this notation called?

v=<x2−x1,y2−y1>v=<x_2-x_1,y_2-y_1>

a)
Vector notation
b)
Scalar notation
c)
Coordinate notation
d)
Matrix notation
69.

Vector notation is for the initial and terminal vector

a)
The initial vector is always longer than the terminal vector.
b)
Initial vector is the endpoint; terminal vector is the starting point.
c)
Initial vector is the starting point; terminal vector is the endpoint.
d)
Both vectors represent the same point in space.
70.

What is the equation v = ai + bj

a)
v = ai + bj is a polynomial equation.
b)
v = ai + bj represents a scalar quantity.
c)
v = ai + bj describes a 3D vector.
d)
v = ai + bj is a vector representation in 2D space.
71.

True or False: Its important to go over your steps carefully!

a)
Careful steps can lead to confusion.
b)
It's not necessary to review your steps.
c)
Going over steps is a waste of time.
d)
True
72.

True or False: Vectors can either be written as coordinates or algebraic expressions

a)
True
b)
Vectors can only be written as numbers
c)
Vectors cannot be expressed algebraically
d)
Vectors are only defined in three dimensions
73.

True or False: Vectors can be used for word problems

a)
Vectors can only be used in physics
b)
Vectors are not applicable to any problems
c)
Vectors are only for mathematical calculations
d)
True
74.

For vectors, the magnitude is really the radius

a)
The magnitude of a vector is its direction.
b)
The magnitude of a vector is the radius.
c)
The magnitude of a vector is always zero.
d)
The magnitude of a vector is the angle.
75.

How should you state direction for vectors? This includes north, west, east, and south

a)
Use cardinal directions (north, south, east, west) and angles as needed.
b)
State directions as left, right, forward, and backward.
c)
Describe direction using colors like red and blue.
d)
Use only numerical values for direction.
76.

How do you memorize west, east, south, north

a)
Use the acronym 'SENW'
b)
Memorize using a map of the world
c)
Count the number of letters in each direction
d)
Use the acronym 'WENS' or visualize a compass.
77.

Never Eat Salty Worms

a)
N, E, W, Z
b)
N, S, E, T
c)
N, E, S, W
d)
N, E, S, A
78.

v=a1i+b1jv=a_1i+b_1j

w=a2i+b2jw=a_2i+b_2j

v⋅w=a1a2+b1b2v\cdot w=a_1a_2+b_1b_2

All these equations are know as...

a)
Vector algebra and dot product formulas
b)
Matrix operations and linear transformations
c)
Scalar multiplication and vector addition
d)
Vector calculus and cross product formulas
79.

What is this equation called?

cos⁡(θ)=(u⋅v)∣u∣∣v∣\cos\left(\theta\right)=\frac{\left(u\cdot v\right)}{\left|u\right|\left|v\right|}

a)
Pythagorean theorem for vectors
b)
Sine formula for vectors
c)
Tangent formula for vectors
d)
Cosine formula for vectors
80.

What makes a vector orthogonal?

a)
The vectors are in the same direction.
b)
The dot product of the vectors is zero.
c)
The vectors are parallel to each other.
d)
The vectors have the same magnitude.
81.

What are two common vector word problems

a)
1. Finding the resultant vector from two vectors. 2. Calculating the angle between two vectors using the dot product.
b)
Determining the slope of a line in a coordinate plane.
c)
Finding the midpoint of a line segment.
d)
Calculating the distance between two points on a graph.
82.

When you aren't able to cancel through system of equations, can't you do substitution with two variable?

a)
Yes, you can use substitution with two variables.
b)
No, substitution is not applicable.
c)
You can only use elimination methods.
d)
Substitution is only for three variables.
83.

What axis do we live in?

a)
Two-dimensional plane (x, y axes)
b)
Three-dimensional space (x, y, z axes)
c)
One-dimensional line (x axis)
d)
Four-dimensional space (x, y, z, w axes)
84.

What does this equation represent?

d=((x2−x1)2+(y2−y1))+(z2−z1)d=\sqrt[]{\left(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)\right)+\left(z_2-z_1\right)}

a)
The area of a triangle in 3D space.
b)
Distance between two points in 3D space.
c)
The volume of a rectangular prism.
d)
The perimeter of a rectangle in 2D space.
85.

If points aren't labeled x1 or x2, you can label them yourself, just be consistant

a)
Do not label the points at all.
b)
Use random letters for labeling points.
c)
Label the points as x1, x2, etc.
d)
Label the points as a1, a2, etc.
86.

What is a position vector?

a)
A position vector is a type of scalar quantity.
b)
A position vector represents the speed of an object.
c)
A position vector is used to calculate the area of a shape.
d)
A position vector indicates the location of a point in space relative to a reference point.
87.

What is the key difference between position vectors and vectors out in space

a)
Position vectors are relative to a reference point; vectors in space can represent any direction and magnitude.
b)
Vectors in space are only used for graphical representation.
c)
Position vectors are always longer than vectors in space.
d)
Position vectors can only point in one direction.
88.

What does this equation represent?

v=(x2−x1)+(y2−y1)+(z2−z1)v=\left(x_2-x_1\right)+\left(y_2-y_1\right)+\left(z_2-z_1\right)

a)
The sum of the coordinates in two-dimensional space.
b)
The average speed of an object in motion.
c)
The total distance traveled in a straight line.
d)
The total displacement in three-dimensional space.
89.

When using the dot product on vectors with 3D, you do the same process, just with an included new variable

a)
The dot product of two 3D vectors is calculated as A · B = a1*b1 + a2*b2 + a3*b3.
b)
The dot product of two 3D vectors is calculated by adding the magnitudes of the vectors.
c)
The dot product requires only two dimensions for calculation.
d)
The dot product of two 3D vectors is calculated as A · B = a1*b1 + a2*b2.
90.

Why is it important to understand the direction of angles?

a)
It is important to understand the direction of angles for accurate geometric interpretation and practical applications.
b)
The direction of angles is irrelevant in real-world applications.
c)
Angles only matter in theoretical mathematics.
d)
Understanding angles is only necessary for advanced physics.
91.

Its okay to used rounded up numbers, but if you can use special right triangles to find results, use them, they are exact for a reason!

a)
Rely solely on calculators for exact results.
b)
Ignore special triangles and use basic arithmetic.
c)
Use only approximate values for calculations.
d)
Use special right triangles for exact results.
92.

cos⁡(a)=a(a2 +b2+c2)\cos\left(a\right)=\frac{a}{\left(\sqrt[]{a^{2\ }+b^2+c^2}\right)} can also be summarized as... (also say it in words)

a)
The cosine of angle 'a' is the product of the lengths of the adjacent and opposite sides.
b)
The cosine of angle 'a' is the sum of the lengths of all sides divided by the hypotenuse.
c)
The cosine of angle 'a' is the ratio of the length of the adjacent side to the length of the hypotenuse.
d)
The cosine of angle 'a' is the ratio of the length of the opposite side to the length of the hypotenuse.
93.

cos⁡(b)=b(a2 +b2+c2)\cos\left(b\right)=\frac{b}{\left(\sqrt[]{a^{2\ }+b^2+c^2}\right)} can be simplified as...... say it in words! Use words to say the answer

a)
The cosine of angle b is the sum of sides a and c divided by side b.
b)
The cosine of angle b is the product of side b and the hypotenuse.
c)
The cosine of angle b is the difference between side b and the hypotenuse.
d)
The cosine of angle b is the length of side b divided by the length of the hypotenuse.
94.

When we enter the 3D in Vectors, the new z value is represented with what variable?

a)
y
b)
x
c)
w
d)

k

95.

cos⁡(c)=c(a2 +b2+c2)\cos\left(c\right)=\frac{c}{\left(\sqrt[]{a^{2\ }+b^2+c^2}\right)} can be simplified to.....

a)
The cosine of angle c is equal to the length of side c divided by the length of the hypotenuse.
b)
The sine of angle c is equal to the length of side c divided by the length of the hypotenuse.
c)
The tangent of angle c is equal to the length of side c multiplied by the length of the hypotenuse.
d)
The cosine of angle c is equal to the length of side a divided by the length of side b.

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