Check the picture below.
[tex]\bf P~(\stackrel{a}{5}~~,~~\stackrel{b}{12})\qquad \impliedby \textit{let's find the hypotenuse} \\\\\\ \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{5^2+12^2}\implies c=\sqrt{25+144}\implies c=\sqrt{169}\implies c=13 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill sin(\theta )=\cfrac{\stackrel{opposite}{12}}{\stackrel{hypotenuse}{13}}\qquad \qquad cos(\theta )=\cfrac{\stackrel{adjacent}{5}}{\stackrel{hypotenuse}{13}}~\hfill[/tex]
Answer:
The answer to your question is:
sin Ф = 12/13
cos Ф = 5/13
Step-by-step explanation:
Data
Point (5,12)
sin Ф = ?
cos Ф = ?
Process
1.- Plot the point, and draw a right triangle from the points (0, 0), (5, 0) and (5, 12). See the picture below.
2.- Calculate the hypotenuse.
3.- Calculate sin Ф and cos Ф.
c² = 5² + 12²
c² = 25 + 144
c² = 169
c = 13
sin Ф = opposite side/ hypotenuse = 12/13
cos Ф = adjacent side/ hypotenuse = 5/13
