Quiz about Unit 6 – Polar Coordinates and Vectors Vocab

Question 1

What is polar coordinates?

Accepted Answer

Polar coordinates are a system for representing points in a plane using a distance and an angle.

Answer

A method for calculating distances in three-dimensional space.

Answer

A way to represent points using only Cartesian coordinates.

Answer

A system that uses only angles to define locations.

Question 2

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

Accepted Answer

The point flips because a negative radius reflects the point across the origin.

Answer

A negative radius has no effect on the point's position.

Answer

A negative radius moves the point to a different quadrant without flipping.

Answer

The point flips because the radius is squared.

Question 3

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

Accepted Answer

Clockwise direction

Answer

Counterclockwise direction

Answer

Diagonal direction

Answer

Straight up direction

Question 4

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

Accepted Answer

Counterclockwise

Answer

Clockwise

Answer

Straight up

Answer

Downward

Question 5

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

Accepted Answer

rcos(x)=x

Answer

rcos(x)=y

Question 6

What equation to find the y value in polar coordinates?

Accepted Answer

rsin(x)=y

Answer

rsin(x)=x

Question 7

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

Accepted Answer

True

Answer

False

Answer

Only for Polar to Rectangle

Answer

Only for Rectangle to Polar

Question 8

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

Accepted Answer

the distance from the origin to a point (x,y) in Cartesian coordinates

Answer

the slope of a line in slope-intercept form

Answer

the area of a circle with radius r

Answer

the perimeter of a rectangle with sides x and y

Question 9

This equation is used to find.... $$ heta= an^{-1}\left(\frac{y}{x} ight)$$

Accepted Answer

The angle $ \theta $ in a right triangle.

Answer

The area of a triangle.

Answer

The length of the hypotenuse.

Answer

The perimeter of a triangle.

Question 10

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

Accepted Answer

Yes, the point flips over the origin.

Answer

The point moves to a different quadrant.

Answer

The point remains unchanged.

Answer

The point disappears from the plane.

Question 11

What are the nine equations of polar equations?

Accepted Answer

Circle, Line, Spiral, Rose curve, Lemniscate, Cardioid, Limacon, Hyperbola, Conic sections.

Answer

Parabola

Answer

Quadratic function

Answer

Ellipse

Question 12

$$ heta=k$$ Is a equation for polar coordinates that is.... line

Accepted Answer

a line at angle k

Answer

a spiral with angle k

Answer

a parabola opening upwards

Answer

a circle with radius k

Question 13

What is a cardiod in math?

Accepted Answer

A cardioid is a heart-shaped curve in mathematics.

Answer

A cardioid is a type of triangle.

Answer

A cardioid is a mathematical function that represents a circle.

Answer

A cardioid is a polygon with four sides.

Question 14

How do you find the radius of $$r=a\cos heta$$

Accepted Answer

$$\left|\frac{a}{2}\right|$$

Answer

$$\frac{a}{2}$$

Question 15

How do you find the center of $$r=a\cos heta$$

Accepted Answer

(a/2, 0)

Answer

(a/2, a/2)

Answer

(a, 0)

Answer

(0, a/2)

Question 16

True or False: $$r=a\cos heta$$ is vertical, not horizontal

Accepted Answer

False

Answer

True

Answer

r=a\sin	heta is vertical

Answer

It is horizontal

Question 17

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

Accepted Answer

True

Answer

The radius can be imaginary

Answer

The radius is always zero

Answer

The radius can be negative in some cases

Question 18

How do you find the radius of $$r=a\sin heta$$

Accepted Answer

$$\left|\frac{a}{2}\right|$$

Answer

$$\frac{a}{2}$$

Question 19

How do you find the center of $$r=a\sin heta$$

Accepted Answer

(0,a/2)

Answer

(a/2,0)

Question 20

What direction will $$r=a\left(1+\cos heta ight)$$ go horizontally.

Accepted Answer

Only right

Answer

Neither right nor left

Answer

Only left

Answer

Both right and left

Question 21

What direction will $$r=a\left(1-\cos heta ight)$$ go horizontally.

Accepted Answer

The direction goes horizontally from left.

Answer

The direction goes horizontally from right to left.

Answer

The direction goes diagonally from bottom left to top right.

Answer

The direction goes vertically from top to bottom.

Question 22

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

Accepted Answer

d = 2a

Answer

d = a/2

Answer

d = 3a

Answer

d = a

Question 23

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

Accepted Answer

a must be greater than b

Answer

a can be any value compared to b

Answer

a must equal b

Answer

a must be less than b

Question 24

$$r=a+b\cos heta$$ and $$r=a-b\cos heta$$ give which direction does it have?

Accepted Answer

The direction is symmetric about the polar axis (x-axis).

Answer

The direction is random and not defined.

Answer

The direction is circular around the origin.

Answer

The direction is vertical along the y-axis.

Question 25

$$r=a+b\sin heta$$ and $$r=a-b\sin heta$$ has a shift in which direction?

Accepted Answer

Vertical shift, with the first curve shifting up and the second curve shifting down.

Answer

No shift, both curves remain unchanged.

Answer

Horizontal shift, with both curves shifting to the right.

Answer

Diagonal shift, with the first curve shifting up and the second curve shifting down.

Question 26

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

Accepted Answer

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

Answer

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

Question 27

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

Accepted Answer

a < b

Answer

a + b = 0

Answer

a > b

Answer

a = b

Question 28

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

Accepted Answer

(a+b)

Answer

(b-a)

Question 29

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

Accepted Answer

(b-a)

Answer

(a+b)

Question 30

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

Accepted Answer

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.

Answer

The Rectangular Plane uses polar coordinates while the Polar Plane uses Cartesian coordinates.

Answer

The Complex Plane is only a one-dimensional representation of complex numbers.

Answer

The Complex Plane is a three-dimensional representation of real numbers.

Question 31

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

Accepted Answer

The real axis.

Answer

The y-axis.

Answer

The imaginary axis.

Answer

The z-axis.

Question 32

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

Accepted Answer

The imaginary part of a complex number.

Answer

The real part of a complex number.

Answer

The modulus of a complex number.

Answer

The angle of a complex number.

Question 33

What is the template for the complex plane equation?

Accepted Answer

z = x + yi

Answer

z = x * yi

Answer

z = x / yi

Answer

z = x - yi

Question 34

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

Accepted Answer

True

Answer

False

Answer

Magnitude is not used in The Complex Plane

Answer

Radius is the only term used in mathematics

Question 35

What variable represents the magnitude in the complex plane?

Accepted Answer

z

Answer

x

Answer

y

Answer

r

Question 36

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

Accepted Answer

True

Answer

The function can be subtracted on both sides

Answer

Factoring is not necessary for solutions

Answer

False

Question 37

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

Accepted Answer

We add 180 degrees to adjust the angle into the correct quadrant for tangent.

Answer

We add 180 degrees to convert to radians.

Answer

We add 180 degrees to find the sine value.

Answer

We add 180 degrees to simplify the angle.

Question 38

What is the De Moivre's Theorme?

Accepted Answer

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).

Answer

De Moivre's Theorem states that all complex numbers are real numbers.

Answer

De Moivre's Theorem is used to calculate the area of triangles.

Answer

De Moivre's Theorem describes the relationship between logarithms and exponential functions.

Question 39

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

Accepted Answer

False

Answer

True

Question 40

What is a vector in precalculus?

Accepted Answer

A vector is a mathematical object with both magnitude and direction.

Answer

A vector is a single point in space.

Answer

A vector is a type of polynomial function.

Answer

A vector is a scalar quantity with no direction.

Question 41

What two points are important to understanding vectors?

Accepted Answer

initial and terminal

Answer

Position and velocity

Answer

Force and mass

Answer

Speed and acceleration

Question 42

What is magnitude in vectors?

Accepted Answer

Magnitude is the length of a vector.

Answer

Magnitude is the sum of the vector components.

Answer

Magnitude is the angle between two vectors.

Answer

Magnitude is the direction of a vector.

Question 43

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

Accepted Answer

Distance formula

Answer

Quadratic equation

Answer

Slope formula

Answer

Pythagorean theorem

Question 44

Where is the distance formula from?

Accepted Answer

The distance formula is derived from the Pythagorean theorem.

Answer

The distance formula is derived from trigonometry.

Answer

The distance formula comes from algebraic equations.

Answer

The distance formula is based on calculus.

Question 45

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

Accepted Answer

True

Answer

The arrow represents magnitude

Answer

The arrow indicates speed

Answer

The arrow shows distance

Question 46

What is the notation to write a vector?

Accepted Answer

Answer

Literally anything else

Question 47

True or False: Vectors can't have operations

Accepted Answer

False

Answer

Vectors have no defined operations

Answer

Vectors can only be multiplied

Answer

Vectors can only be added

Question 48

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

Accepted Answer

the terminal point of the first vector

Answer

the endpoint of the second vector

Answer

the midpoint of the first vector

Answer

the initial point of the second vector

Question 49

What is negative vector?

Accepted Answer

A vector with the opposite direction to a given vector.

Answer

A vector with the same direction as a given vector.

Answer

A vector that has no direction or magnitude.

Answer

A scalar quantity that represents magnitude only.

Question 50

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

Accepted Answer

Negative vectors can be treated as adding a negative number.

Answer

Negative vectors can only be subtracted from other vectors.

Answer

Adding a negative vector always results in a positive vector.

Answer

Negative vectors have no effect on vector addition.

Question 51

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

Accepted Answer

True

Answer

Adding two vectors is the same as subtracting their magnitudes

Answer

Subtracting two vectors always results in a positive vector

Answer

Subtracting vectors is the same as multiplying by a scalar

Question 52

What is this notation called?

$$v=$$

Accepted Answer

Vector notation

Answer

Scalar notation

Answer

Coordinate notation

Answer

Matrix notation

Question 53

Vector notation is for the initial and terminal vector

Accepted Answer

Initial vector is the starting point; terminal vector is the endpoint.

Answer

The initial vector is always longer than the terminal vector.

Answer

Initial vector is the endpoint; terminal vector is the starting point.

Answer

Both vectors represent the same point in space.

Question 54

What is the equation v = ai + bj

Accepted Answer

v = ai + bj is a vector representation in 2D space.

Answer

v = ai + bj is a polynomial equation.

Answer

v = ai + bj represents a scalar quantity.

Answer

v = ai + bj describes a 3D vector.

Question 55

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

Accepted Answer

True

Answer

Careful steps can lead to confusion.

Answer

It's not necessary to review your steps.

Answer

Going over steps is a waste of time.

Question 56

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

Accepted Answer

True

Answer

Vectors can only be written as numbers

Answer

Vectors cannot be expressed algebraically

Answer

Vectors are only defined in three dimensions

Question 57

True or False: Vectors can be used for word problems

Accepted Answer

True

Answer

Vectors can only be used in physics

Answer

Vectors are not applicable to any problems

Answer

Vectors are only for mathematical calculations

Question 58

For vectors, the magnitude is really the radius

Accepted Answer

The magnitude of a vector is the radius.

Answer

The magnitude of a vector is its direction.

Answer

The magnitude of a vector is always zero.

Answer

The magnitude of a vector is the angle.

Question 59

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

Accepted Answer

Use cardinal directions (north, south, east, west) and angles as needed.

Answer

State directions as left, right, forward, and backward.

Answer

Describe direction using colors like red and blue.

Answer

Use only numerical values for direction.

Question 60

How do you memorize west, east, south, north

Accepted Answer

Use the acronym 'WENS' or visualize a compass.

Answer

Use the acronym 'SENW'

Answer

Memorize using a map of the world

Answer

Count the number of letters in each direction

Question 61

Never Eat Salty Worms

Accepted Answer

N, E, S, W

Answer

N, E, W, Z

Answer

N, S, E, T

Answer

N, E, S, A

Question 62

$$v=a_1i+b_1j$$

$$w=a_2i+b_2j$$

$$v\cdot w=a_1a_2+b_1b_2$$

All these equations are know as...

Accepted Answer

Vector algebra and dot product formulas

Answer

Matrix operations and linear transformations

Answer

Scalar multiplication and vector addition

Answer

Vector calculus and cross product formulas

Question 63

What is this equation called?

$$\cos\left( heta ight)=\frac{\left(u\cdot v ight)}{\left|u ight|\left|v ight|}$$

Accepted Answer

Cosine formula for vectors

Answer

Pythagorean theorem for vectors

Answer

Sine formula for vectors

Answer

Tangent formula for vectors

Question 64

What makes a vector orthogonal?

Accepted Answer

The dot product of the vectors is zero.

Answer

The vectors are in the same direction.

Answer

The vectors are parallel to each other.

Answer

The vectors have the same magnitude.

Unit 6 – Polar Coordinates and Vectors Vocab

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