Question

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.

Answer 1

check the picture below.


`\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=√(a^2+b^2) \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}`


`\bf c=√(1^2+(-1)^2)\implies c=√(2) \\\\\\ sin(\theta )=\cfrac{\stackrel{opposite}{-1}}{\stackrel{hypotenuse}{√(2)}}\implies \stackrel{\textit{rationalizing the denominator}}{\cfrac{-√(2)}{2}} \\\\\\ cos(\theta )=\cfrac{\stackrel{adjacent}{1}}{\stackrel{hypotenuse}{√(2)}}\implies \stackrel{\textit{rationalizing the denominator}}{\cfrac{√(2)}{2}} \\\\\\ tan(\theta )=\cfrac{\stackrel{opposite}{-1}}{\stackrel{adjacent}{1}}\implies -1`