Question

The terminal ray of an angle passes through the point

Answer 1

`(\stackrel{\stackrel{ adjacent }{x}}{-3}~~,~~\stackrel{\stackrel{ opposite }{y}}{-√(7)})\hspace{5em}\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}{-3}\\ o=\stackrel{opposite}{-√(7)} \end{cases}`

`c=\sqrt{ (-3)^2 + (-√(7))^2}\implies c=√( 9 + 7 ) \implies c=√( 16 )\implies c=4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cos(\theta )=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{4}}~\hfill`