text: # What is cos^theta in terms of sintheta?
  
  Dec 18, 2015
  
  If $\theta$ is in Q1 or Q4 then $\cos \theta = \sqrt{1 - {\sin}^{2} \theta}$
  
  If $\theta$ is in Q2 or Q3 then $\cos \theta = - \sqrt{1 - {\sin}^{2} \theta}$
  
  #### Explanation:
  
  We always have ${\cos}^{2} \theta + {\sin}^{2} \theta = 1$ regardless of which quadrant $\theta$ is in. Hence we always have:
  
  $\cos \theta = \pm \sqrt{1 - {\sin}^{2} \theta}$
  
  If $\theta$ is in Q1 or Q4 then $\cos \theta \ge 0$, hence:
  
  $\cos \theta = \sqrt{1 - {\sin}^{2} \theta}$
  
  If $\theta$ is in Q2 or Q3 then $\cos \theta \le 0$, hence:
  
  $\cos \theta = - \sqrt{1 - {\sin}^{2} \theta}$