Convert the point to polar coordinates.(−1,−3)(-1,-\sqrt{3})(−1,−3)

(2,4π3)(2,\frac{4\pi}{3})(2,34π)

Convert the point to polar coordinates. ( − 1 , − 3 ) (-1,-\sqrt{3}) ( − 1 , − 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> )

Here we're asked to convert the point given in rectangular coordinates into polar coordinates, and the point that we're given is the negative one negative square root of 3. So let's start with step number 1 and plot our point. Now it may not be easy to locate the square root of 3 on your graph, but you can always type this into your calculator and you would get that this is equal to about negative 1.73. So with that in mind, graphing this point at negative 1, negative 1.73, we end up right about here in quadrant 3. Now we can move on to step number 2 in calculating r. Now in calculating r, I get that r is equal to that x value negative one squared plus that y value negative root three squared. Now in actually squaring these values, this ends up giving me the square root of 1 +3, which is really just the square root of 4, which we know is just 2. So my r value here is 2, and we can go ahead and move on to step number 3 in finding theta. Now looking at the location of our point here, I see that it's located in quadrant 3. Now because it's located in quadrant 3, that tells me that I need to take the inverse tangent of y over x and then add pi to it. So let's go ahead and do that here. Now here theta will be equal to the inverse tangent of my y value negative root 3 over negative 1. And remember we're going to add pi after we take that inverse tangent. Now taking the inverse tangent here ends up giving me the inverse tangent of the square root of 3, still adding that pi to the end, and the inverse tangent of the square root of 3 is simply pi over 3. So pi over 3 plus pi, making sure to add that factor to get our point located in the right quadrant. This ends up giving me 4pi over 3 for my angle theta. Now I my point in polar coordinates, 24pi over 3, and this is my final answer. Let me know if you have any questions. Thanks for watching.

Convert the point to polar coordinates.(−1,−3)(-1,-\sqrt{3})(−1,−3)

(2,4π3)(2,\frac{4\pi}{3})(2,34π)

(2,π3)(2,\frac{\pi}{3})(2,3π)

(2,7π6)(2,\frac{7\pi}{6})(2,67π)

(−2,4π3)(-2,\frac{4\pi}{3})(−2,34π)

Table of contents

Skip topic navigation

0. Fundamental Concepts of Algebra3h 32m

Algebraic Expressions
37m

Exponents
32m

Polynomials Intro
19m

Multiplying Polynomials
36m

Factoring Polynomials
2m

Radical Expressions
15m

Simplifying Radical Expressions
31m

Rationalize Denominator
15m

Rational Exponents
4m

Pythagorean Theorem & Basics of Triangles
17m

1. Equations and Inequalities3h 27m

Linear Equations
31m

Rational Equations
21m

The Imaginary Unit
6m

Powers of i
11m

Complex Numbers
42m

Intro to Quadratic Equations
18m

The Square Root Property
11m

Completing the Square
12m

The Quadratic Formula
19m

Choosing a Method to Solve Quadratics
9m

Linear Inequalities
22m

2. Graphs1h 43m

Graphs and Coordinates
7m

Two-Variable Equations
23m

Lines
1h 12m

3. Functions & Graphs2h 17m

Intro to Functions & Their Graphs
35m

Common Functions
5m

Transformations
45m

Function Operations
21m

Function Composition
29m

4. Polynomial Functions1h 54m

Quadratic Functions
49m

Understanding Polynomial Functions
34m

Graphing Polynomial Functions
30m

5. Rational Functions1h 23m

Introduction to Rational Functions
9m

Asymptotes
35m

Graphing Rational Functions
38m

6. Exponential and Logarithmic Functions2h 28m

Introduction to Exponential Functions
9m

Graphing Exponential Functions
25m

The Number e
8m

Introduction to Logarithms
22m

Graphing Logarithmic Functions
18m

Properties of Logarithms
27m

Solving Exponential and Logarithmic Equations
35m

7. Measuring Angles40m

Angles in Standard Position
12m

Coterminal Angles
8m

Complementary and Supplementary Angles
10m

Radians
8m

8. Trigonometric Functions on Right Triangles2h 5m

Trigonometric Functions on Right Triangles
45m

Special Right Triangles
30m

Cofunctions of Complementary Angles
26m

Solving Right Triangles
23m

9. Unit Circle1h 19m

Defining the Unit Circle
14m

Trigonometric Functions on the Unit Circle
9m

Common Values of Sine, Cosine, & Tangent
11m

Reference Angles
38m

Reciprocal Trigonometric Functions on the Unit Circle
6m

10. Graphing Trigonometric Functions1h 19m

Graphs of the Sine and Cosine Functions
32m

Phase Shifts
14m

Graphs of Secant and Cosecant Functions
10m

Graphs of Tangent and Cotangent Functions
21m

11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m

Inverse Sine, Cosine, & Tangent
28m

Evaluate Composite Trig Functions
44m

Linear Trigonometric Equations
28m

12. Trigonometric Identities 2h 34m

Introduction to Trigonometric Identities
1h 4m

Sum and Difference Identities
1h 3m

Double Angle Identities
16m

Solving Trigonometric Equations Using Identities
9m

13. Non-Right Triangles1h 38m

Law of Sines
49m

Law of Cosines
30m

Area of SAS & ASA Triangles
19m

14. Vectors2h 25m

Geometric Vectors
28m

Vectors in Component Form
32m

Direction of a Vector
23m

Unit Vectors and i & j Notation
27m

Dot Product
22m

Cross Product
11m

15. Polar Equations2h 5m

Polar Coordinate System
29m

Convert Points Between Polar and Rectangular Coordinates
26m

Convert Equations Between Polar and Rectangular Forms
29m

Graphing Other Common Polar Equations
39m

16. Parametric Equations1h 6m

Graphing Parametric Equations
12m

Eliminate the Parameter
32m

Writing Parametric Equations
21m

17. Graphing Complex Numbers1h 7m

Graphing Complex Numbers
6m

Polar Form of Complex Numbers
22m

Products and Quotients of Complex Numbers
14m

Powers of Complex Numbers (DeMoivre's Theorem)
23m

18. Systems of Equations and Matrices3h 6m

Two Variable Systems of Linear Equations
8m

Introduction to Matrices
1h 11m

Determinants and Cramer's Rule
1h 3m

Graphing Systems of Inequalities
42m

19. Conic Sections2h 36m

Introduction to Conic Sections
6m

Circles
26m

Ellipses: Standard Form
33m

Parabolas
36m

Hyperbolas at the Origin
40m

Hyperbolas NOT at the Origin
12m

20. Sequences, Series & Induction1h 15m

Sequences
33m

Arithmetic Sequences
25m

Geometric Sequences
15m

21. Combinatorics and Probability1h 45m

Factorials
11m

Combinatorics
46m

Probability
47m

22. Limits & Continuity1h 49m

Introduction to Limits
41m

Finding Limits Algebraically
40m

Continuity
27m

23. Intro to Derivatives & Area Under the Curve2h 9m

Tangent Lines & Derivatives
44m

Limits at Infinity
18m

Limits of Sequences
9m

Area Under a Curve
56m

OLD 1. Fundamental Concepts of Algebra Coming soon

Models and Applications

Linear Inequalities and Absolute Value Inequalities

OLD 2. Functions and Graphs Coming soon

Distance and Midpoint Formulas, Circles

Modeling with Functions

OLD 3. Polynomial and Rational Functions Coming soon

OLD 4. Exponential and Logarithmic Functions Coming soon

OLD 5. Trigonometric Functions Coming soon

OLD 6. Analytic Trigonometry Coming soon

OLD 7. Additional Topics in Trigonometry Coming soon

OLD 8. Systems of Equations and Inequalities Coming soon

OLD 9. Matrices and Determinants Coming soon

OLD 10. Conic Sections and Analytic Geometry Coming soon

OLD 11. Sequences, Induction, and Probability Coming soon

OLD 12. Introduction to Calculus Coming soon

15. Polar Equations

Convert Points Between Polar and Rectangular Coordinates

Precalculus

15. Polar Equations

Convert Points Between Polar and Rectangular Coordinates

Previous problemNext problem

Struggling with Precalculus?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

Convert the point to polar coordinates.
$(-1,-$\sqrt{3}$)$

$(2,$\frac{\pi}{3}$)$

$(2,$\frac{7\pi}{6}$)$

$(2,$\frac{4\pi}{3}$)$

$(-2,$\frac{4\pi}{3}$)$

0 Comments

Previous problemNext problem

Verified step by step guidance

Identify the given Cartesian coordinates, which are (-1, -√3).

Use the formula for converting Cartesian coordinates to polar coordinates: r = √(x² + y²) and θ = arctan(y/x).

Calculate the radius r: r = √((-1)² + (-√3)²) = √(1 + 3) = √4 = 2.

Determine the angle θ: θ = arctan((-√3)/(-1)) = arctan(√3). Since the point is in the third quadrant, adjust the angle to θ = π + π/3 = 4π/3.

Combine the radius and angle to express the point in polar coordinates: (r, θ) = (2, 4π/3).

2:21m

Watch next

Master Convert Points from Rectangular to Polar Example 1 with a bite sized video explanation from Patrick Ford

Convert Points Between Polar and Rectangular Coordinates practice set

Problem sets built by lead tutors

Expert video explanations

Download the Mobile app

Accessibility

Privacy

Do not sell my personal information

Struggling with Precalculus?

Convert the point to polar coordinates.(−1,−3)(-1,-\(\sqrt{3}\))(−1,−3)

Watch next

Convert Points Between Polar and Rectangular Coordinates practice set

Convert the point to polar coordinates.
$(-1,-\(\sqrt{3}\))$