Question

Round to ten-thousandth (cut off says quadrant 1, I couldnt fit it all in.)

Answer 1

sin(A)=2/5

trig identity:

* sin^2(A)+cos^2(A)=1

* tan(A)=sin(A)/cos(A)

find: tan(A)

`\begin{gathered} \sin ^2(A)+\cos ^2(A)=1 \\ ((2)/(5))^2+\cos ^2(A)=1 \\ \cos ^2(A)=1-(4)/(25) \\ \cos ^2(A)=(21)/(25) \\ \cos (A)=\sqrt[]{(21)/(25)}=\frac{\sqrt[]{21}}{5} \end{gathered}`
`\begin{gathered} \tan (A)=(\sin (A))/(\cos (A)) \\ \tan (A)=\frac{(2)/(5)}{\frac{\sqrt[]{21}}{5}} \\ \tan (A)=\frac{2}{\sqrt[]{21}}\approx0.436 \end{gathered}`