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

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

the slope of a line in slope-intercept form

the area of a circle with radius r

the perimeter of a rectangle with sides x and y

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

The angle $ \theta $ in a right triangle.

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

Yes, the point flips over the origin.

The point moves to a different quadrant.

The point disappears from the plane.

What are the nine equations of polar equations?

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

What is a vertical equation for polar equations?

r = cos(θ) for a vertical line in polar coordinates.

r = sin(θ) for a vertical line in polar coordinates.

r = θ for a vertical line in polar coordinates.

What is a cardiod in math?

A cardioid is a heart-shaped curve in mathematics.

A cardioid is a type of triangle.

A cardioid is a mathematical function that represents a circle.

A cardioid is a polygon with four sides.

What is limacon w/out inner loop?

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.

A limacon that is a straight line defined by r = 0.

A limacon with an inner loop defined by r = a - b*cos(θ) or r = a - b*sin(θ) with a < b.

A limacon defined by r = a + b*cos(θ) or r = a + b*sin(θ) with a = b.

What is limacon w/inner loop?

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.

A limacon with an inner loop is a straight line in polar coordinates.

A limacon with an inner loop is defined by r = a - b * cos(θ) with a > b.

A limacon with an inner loop is a type of ellipse in Cartesian coordinates.

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

The radius can be negative in some cases

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

The direction goes horizontally from left.

The direction goes horizontally from right to left.

The direction goes diagonally from bottom left to top right.

The direction goes vertically from top to bottom.

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

a can be any value compared to b

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

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

The direction is random and not defined.

The direction is circular around the origin.

The direction is vertical along the y-axis.

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

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

No shift, both curves remain unchanged.

Horizontal shift, with both curves shifting to the right.

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

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

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

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

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

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.

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

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

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

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

The imaginary part of a complex number.

The real part of a complex number.

The modulus of a complex number.

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

Magnitude is not used in The Complex Plane

Radius is the only term used in mathematics

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

The function can be subtracted on both sides

Factoring is not necessary for solutions

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

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

We add 180 degrees to convert to radians.

We add 180 degrees to find the sine value.

We add 180 degrees to simplify the angle.

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?

Add 180 degrees (or π radians) to the angle.

Add 90 degrees (or π/2 radians) to the angle.

Subtract 180 degrees (or π radians) from the angle.

Add 360 degrees (or 2π radians) to the angle.

How do you convert polar plane to complex plane?

z = r * (cos(θ) + i * sin(θ)) or z = r * e^(iθ)

z = r * (tan(θ) + i * sec(θ))

z = r * (sin(θ) - i * cos(θ))

What is the De Moivre's Theorme?

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).

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

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

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

What is a vector in precalculus?

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

A vector is a single point in space.

A vector is a type of polynomial function.

A vector is a scalar quantity with no direction.

Unit 6 – Polar Coordinates and Vectors Vocab

Authored by Leonel Roman Avalos

Mathematics

12th Grade

CCSS covered

Used 33+ times

Unit 6 – Polar Coordinates and Vectors Vocab

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Unit 6 will inform us about polar coordinates, their representation, and operations involving vectors in polar form.

Unit 6 will focus on the history of mathematics.

Unit 6 will cover basic algebra and its applications.

Unit 6 will teach about three-dimensional geometry.

Tags

CCSS.HSN.CN.B.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is polar coordinates?

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

A method for calculating distances in three-dimensional space.

A way to represent points using only Cartesian coordinates.

A system that uses only angles to define locations.

Tags

CCSS.HSN.CN.B.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the two parts of a polar coordinate pair?

The two parts are the diameter (d) and the height (h).

The two parts are the base (b) and the exponent (e).

The two parts are the radius (r) and the angle (θ).

The two parts are the length (l) and the width (w).

Tags

CCSS.HSN.CN.B.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

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

The point flips because the radius is squared.

Tags

CCSS.HSN.CN.B.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Counterclockwise direction

Diagonal direction

Clockwise direction

Straight up direction

Tags

CCSS.HSN.CN.B.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Clockwise

Straight up

Downward

Counterclockwise

Tags

CCSS.HSN.CN.B.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

rcos(x)=x

rcos(x)=y

Tags

CCSS.HSF.TF.B.7

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Unit 6 – Polar Coordinates and Vectors Vocab

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

What is polar coordinates?

What are the two parts of a polar coordinate pair?

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

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

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

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

What equation to find the y value in polar coordinates?

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

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