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