Question

find the exact value of each of the remainning trig functions of theta. sin theta = 12/13 in Quadrant 2

Answer 1

\(\bf sin(\theta)=\cfrac{12}{13}\implies \cfrac{\textit{opposite side}}{\textit{hypotenuse}}\implies \cfrac{b}{c}\\ \quad \\
\textit{how to find the 3rd side "a" ?}\\ \quad \\
c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\\ \quad \\
\textit{recall, we're on the 2nd Quadrant, so "a" will be negative }\\ \quad \\
-\sqrt{c^2-b^2}=a\)

once you find all sides, "a", "b" and "c", then use the trig ratios to get them all http://htmartin.myweb.uga.edu/6190/resources/Trig%20Functions.gif

Answer 2

yea i got the final side length of the triangle is 5, im just confused what it means when it asks to find the exact value of each trig f-n of theta