Question

trigonometry problem. I had to ask it like this because I can't type fractions on my phone. the last bit just says round to ten-thousandth

Answer 1

To find tan (A) we already have the value of sin(A) but we have to find cos(A) so we can use hte identity:

$\sin ^2(A)+\cos ^2(A)=1$

to find cos(A) by replacing the value of Sin(A) so:

$(\frac{3}{4})^2+\cos ^2(A)=1$

and we solve for cos(A) so:

$\begin{gathered} \frac{9}{16}+\cos ^2(A)=1 \\ \cos ^2(A)=\frac{16}{16}-\frac{9}{16} \\ \cos (A)=\sqrt[]{\frac{7}{16}}=\frac{\sqrt[]{7}}{4} \end{gathered}$

Now we can fin tan(A) so:

$\begin{gathered} \tan (A)=\frac{\sin(A)}{\cos(A)} \\ \tan (A)=\frac{\frac{3}{4}}{\frac{\sqrt[]{7}}{4}} \\ \tan (A)=\frac{3}{\sqrt[]{7}} \\ \tan (A)=\frac{3\sqrt[]{7}}{7} \\ \tan (A)=1.1339 \end{gathered}$