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The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

Respuesta :

check the picture below.

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\bf c=\sqrt{1^2+(-1)^2}\implies c=\sqrt{2} \\\\\\ sin(\theta )=\cfrac{\stackrel{opposite}{-1}}{\stackrel{hypotenuse}{\sqrt{2}}}\implies \stackrel{\textit{rationalizing the denominator}}{\cfrac{-\sqrt{2}}{2}} \\\\\\ cos(\theta )=\cfrac{\stackrel{adjacent}{1}}{\stackrel{hypotenuse}{\sqrt{2}}}\implies \stackrel{\textit{rationalizing the denominator}}{\cfrac{\sqrt{2}}{2}} \\\\\\ tan(\theta )=\cfrac{\stackrel{opposite}{-1}}{\stackrel{adjacent}{1}}\implies -1[/tex]
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