Answer:
The answer are the options B and C
[tex]sin(x)=\frac{5}{13}[/tex]
[tex]tan(x)=\frac{5}{12}[/tex]
Step-by-step explanation:
we know that
[tex]csc(x)=\frac{1}{sin(x)}[/tex]
In this problem we have
[tex]csc(x)=\frac{13}{5}[/tex]
substitute
[tex]\frac{13}{5}=\frac{1}{sin(x)}[/tex]
solve for sin(x)
[tex]sin(x)=\frac{5}{13}[/tex]
[tex]cos^{2}(x)+sin^{2}(x)=1[/tex]
substitute the value of sin(x) and solve for cos(x)
[tex]cos^{2}(x)+(\frac{5}{13})^{2}=1[/tex]
[tex]cos^{2}(x)=1-(\frac{5}{13})^{2}[/tex]
[tex]cos^{2}(x)=(\frac{13^{2}-5^{2}}{13^{2}})[/tex]
[tex]cos^{2}(x)=(\frac{144}{13^{2}})[/tex]
[tex]cos^{2}(x)=(\frac{12^{2}}{13^{2}})[/tex]
[tex]cos(x)=(\frac{12}{13})[/tex]
The function tangent is equal to
[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]
substitute the values
[tex]tan(x)=\frac{(5/13)}{(12/13)}=5/12[/tex]
