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:

`((3)/(4))^2+\cos ^2(A)=1`

and we solve for cos(A) so:

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

Now we can fin tan(A) so:

`\begin{gathered} \tan (A)=(\sin(A))/(\cos(A)) \\ \tan (A)=\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}`