# How do you convert (2,(-7pi)/6) into cartesian form?

May 10, 2017

Use $x = r \cos \theta$ and $y = r \sin \theta$. Answer: $\left(- \sqrt{3} , 1\right)$

#### Explanation:

Original problem: Convert $\left(2 , - \frac{7 \pi}{6}\right)$ to Cartesian

To convert from polar coordinates to Cartesian form, we use the equations $x = r \cos \theta$ and $y = r \sin \theta$.

Since we have $\left(r , \theta\right)$, we can simply substitute into the above formulas:
$x = 2 \cos \left(- \frac{7 \pi}{6}\right)$
Using our unit circle trig values
$x = 2 \left(- \frac{\sqrt{3}}{2}\right)$
$x = - \sqrt{3}$

$y = 2 \sin \left(- \frac{7 \pi}{6}\right)$
Using our unit circle trig values
$y = 2 \left(\frac{1}{2}\right)$
$y = 1$

Therefore our final answer in Cartesian form is: $\left(- \sqrt{3} , 1\right)$
The text passage contains a mathematical question about converting polar coordinates to Cartesian form, and it provides a detailed step-by-step solution to the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
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- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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# How do you convert (2,(-7pi)/6) into cartesian form?

May 10, 2017

Use $x = r \cos \theta$ and $y = r \sin \theta$. Answer: $\left(- \sqrt{3} , 1\right)$

#### Explanation:

Original problem: Convert $\left(2 , - \frac{7 \pi}{6}\right)$ to Cartesian

To convert from polar coordinates to Cartesian form, we use the equations $x = r \cos \theta$ and $y = r \sin \theta$.

Since we have $\left(r , \theta\right)$, we can simply substitute into the above formulas:
$x = 2 \cos \left(- \frac{7 \pi}{6}\right)$
Using our unit circle trig values
$x = 2 \left(- \frac{\sqrt{3}}{2}\right)$
$x = - \sqrt{3}$

$y = 2 \sin \left(- \frac{7 \pi}{6}\right)$
Using our unit circle trig values
$y = 2 \left(\frac{1}{2}\right)$
$y = 1$

Therefore our final answer in Cartesian form is: $\left(- \sqrt{3} , 1\right)$
user
The text passage contains a mathematical question about converting polar coordinates to Cartesian form, and it provides a detailed step-by-step solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER