text: # 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: $\left(- \sqrt{3} , 1\right)$
explanation: The document contains a math question and its corresponding answer. The question asks how to convert the polar coordinates \((2, -\frac{7\pi}{6})\) into Cartesian form, and the answer is provided as \((- \sqrt{3}, 1)\).
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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: $\left(- \sqrt{3} , 1\right)$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding answer. The question asks how to convert the polar coordinates \((2, -\frac{7\pi}{6})\) into Cartesian form, and the answer is provided as \((- \sqrt{3}, 1)\).
  
  Label: question-and-answer