text: # 4cos^2x−3=0
  
  Question
  Trigonometric Functions
  $$\displaystyle{4}{{\cos}^{{2}}{x}}−{3}={0}$$
  
  2021-03-07
  $$\displaystyle{4}{\left({\cos}^{{2}}\right)}{x}-{3}={0}$$
  $$\displaystyle{4}{\left({\cos}^{{2}}\right)}={3}$$
  $$\displaystyle{\left({\cos}^{{2}}\right)}{x}=\frac{{3}}{{4}}$$
  $$\displaystyle{\cos{{x}}}=\frac{{\sqrt{{3}}}}{{2}}$$
  $$\displaystyle{x}={{\cos}^{{-{{1}}}}{\left(\frac{{\sqrt{{3}}}}{{2}}\right)}}$$
  x=30
  
  ### Relevant Questions
  
  Which statement cannot be true? Explain.
  A. $$\displaystyle{\sin{{A}}}={0.5}$$
  B. $$\displaystyle{\sin{{A}}}={1.2654}$$
  C. $$\displaystyle{\sin{{A}}}={0.9962}$$
  D. PSKsin A = 3/4
  Let theta be an angle in standard position, $$\displaystyle{\sin{\theta}}{<}{0},{\cos{\theta}}{>}{0}$$. Name the quadrant in which theta lies.
  Given the following information about one trigonometric function, evaluate the other five functions.
  $$\displaystyle{\cos{{u}}}=\frac{{5}}{{13}}$$ , where $$\displaystyle{0}\le{u}\le\frac{\pi}{{2}}.$$
  Find the values of the other trigonometric functions of theta if $$\displaystyle{\cot{\theta}}=-\frac{{4}}{{3}}{\quad\text{and}\quad}{\sin{\theta}}{<}{0}$$.
  If $$f(\theta) = \sin \theta = 0.2$$
  Find $$f(\theta + \pi)$$
  $$y=\sin(\pi x)$$
  When using the half-angle formulas for trigonometric functions of $$alpha/2$$, I determine the sign based on the quadrant in which $$alpha$$ lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
  Find derivative of trigonometric function $$y=(3(1-sin x))/(2cos x)$$
explanation: The provided text is a math problem and its solution. The problem is to solve the trigonometric equation \(4\cos^2(x) - 3 = 0\). The solution steps are given, leading to the answer \(x = 30^\circ\).
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: # 4cos^2x−3=0
  
  Question
  Trigonometric Functions
  $$\displaystyle{4}{{\cos}^{{2}}{x}}−{3}={0}$$
  
  2021-03-07
  $$\displaystyle{4}{\left({\cos}^{{2}}\right)}{x}-{3}={0}$$
  $$\displaystyle{4}{\left({\cos}^{{2}}\right)}={3}$$
  $$\displaystyle{\left({\cos}^{{2}}\right)}{x}=\frac{{3}}{{4}}$$
  $$\displaystyle{\cos{{x}}}=\frac{{\sqrt{{3}}}}{{2}}$$
  $$\displaystyle{x}={{\cos}^{{-{{1}}}}{\left(\frac{{\sqrt{{3}}}}{{2}}\right)}}$$
  x=30
  
  ### Relevant Questions
  
  Which statement cannot be true? Explain.
  A. $$\displaystyle{\sin{{A}}}={0.5}$$
  B. $$\displaystyle{\sin{{A}}}={1.2654}$$
  C. $$\displaystyle{\sin{{A}}}={0.9962}$$
  D. PSKsin A = 3/4
  Let theta be an angle in standard position, $$\displaystyle{\sin{\theta}}{<}{0},{\cos{\theta}}{>}{0}$$. Name the quadrant in which theta lies.
  Given the following information about one trigonometric function, evaluate the other five functions.
  $$\displaystyle{\cos{{u}}}=\frac{{5}}{{13}}$$ , where $$\displaystyle{0}\le{u}\le\frac{\pi}{{2}}.$$
  Find the values of the other trigonometric functions of theta if $$\displaystyle{\cot{\theta}}=-\frac{{4}}{{3}}{\quad\text{and}\quad}{\sin{\theta}}{<}{0}$$.
  If $$f(\theta) = \sin \theta = 0.2$$
  Find $$f(\theta + \pi)$$
  $$y=\sin(\pi x)$$
  When using the half-angle formulas for trigonometric functions of $$alpha/2$$, I determine the sign based on the quadrant in which $$alpha$$ lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
  Find derivative of trigonometric function $$y=(3(1-sin x))/(2cos x)$$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a math problem and its solution. The problem is to solve the trigonometric equation \(4\cos^2(x) - 3 = 0\). The solution steps are given, leading to the answer \(x = 30^\circ\).
  
  Label: question-and-answer