Question

If tan x = 1, what is the value of csc x?​

Answer 1

`\tan(x)=1\implies \tan(x )=\cfrac{\stackrel{opposite}{1}}{\underset{adjacent}{1}}\qquad \textit{let's find the \underline{hypotenuse}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=√(a^2 + o^2) \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{1}\\ o=\stackrel{opposite}{1} \end{cases}`

`c=√( 1^2 + 1^2)\implies c=√( 1 + 1 ) \implies c=√( 2 ) \\\\[-0.35em] ~\dotfill\\\\ \csc(x )=\cfrac{\stackrel{hypotenuse}{√(2)}}{\underset{opposite}{1}}\implies \csc(x )=√(2)`