#9. Inverse Trig Compositions with Variables 1

 $\sin\left(\cos^{-1}\left(x\right)\right)$  is

•  $\sqrt{1-x^2}$  

•  $\frac{1}{\pm\sqrt{1-x^2}}$  

•  $\pm\sqrt{1-x^2}$  

•  $\frac{1}{\sqrt{1-x^2}}$  

 $\cos\left(\cot^{-1}\left(x\right)\right)$  is

•  $\frac{\sqrt{1+x^2}}{x}$  

•  $\frac{x}{\sqrt{1+x^2}}$  

• None of the two the answer needs an absolute value

• None of the two the answer needs a  $\pm$  

 $\sin\left(\tan^{-1}\left(\frac{1}{x}\right)\right)$  is

•  $\frac{\sqrt{1+x^2}}{1}$  

•  $\pm\frac{1}{\sqrt{1+x^2}}$  

• None of the two the answer needs an absolute value

• None of the two the answer needs a  $\pm$  but the not the fraction shown 

 $\cot\left(\operatorname{arcsec}\left(\frac{3x}{4}\right)\right)$  is

•  $\frac{\sqrt{16+9x^2}}{4}$  

•  $\pm\frac{4}{\sqrt{16+9x^2}}$  

• None of the two the answer needs an absolute value

• None of the two the answer needs a  $\pm$  but the not the fraction shown 

 $\csc\left(\arccos\left(\frac{3}{2x}\right)\right)$  is

•  $\pm\frac{\sqrt{4x^2-9}}{2x}$  

•  $\left|\frac{\sqrt{4x^2-9}}{2x}\right|$  

•  $\pm\frac{2x}{\sqrt{4x^2-9}}$  

•  $\left|\frac{2x}{\sqrt{4x^2-9}}\right|$  

 $\cos\left(\csc\left(\frac{x}{\sqrt{x^2-4}}\right)\right)$  is

•  $\pm\frac{2}{x}$  

•  $\left|\frac{2}{x}\right|$  

•  $\pm\frac{x}{2}$  

•  $\left|\frac{x}{2}\right|$  

• The answwr is not here, it does not requires either  $\pm$  nor Absolute Value

 $\tan\left(\cot^{-1}\left(\frac{1}{x+2}\right)\right)$  is

•  $\pm\left(x+2\right)$ 

•  $\left|x+2\right|$ 

•  $x+2$ 

• The answer is not here

If   $f\left(x\right)$  is the trig function and $g\left(x\right)\$  is an inverse trig function , which statement is NOT true when evaluating  $f\left(g\left(x\right)\right)$  

•  $g\left(x\right)$   determines the quadrants where the solution is

• f(x) determines if the final answer is always positive or not

• If  $g\left(x\right)\ has\ a\ PI\ of\ \left(-\frac{\pi}{2},\ \frac{\pi}{2}\right)$  then the answer is always positive

• The answer needs  $\pm$  if does not contain a linear term   $x$ in either numerator or denominator  and if  $f\left(x\right)\$  is either  positive or negative within the PI of  $g\left(x\right)$