Question

Check all that apply. If csc =13/5 , then:

Answer 1

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

$tan(x)=\frac{(5/13)}{(12/13)}=5/12$

Answer 2

Answers: (A) Sin = 5/13 and (B) tan = 5/12