Question

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

A. cos =5/13
B. sin = 5/13
C. tan = 5/12
D. sec = 5/13

Answer 1

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

Answer 2

The answer are the options B and C

`sin(x)=(5)/(13)`

`tan(x)=(5)/(12)`

Explanation:

we know that

`csc(x)=(1)/(sin(x))`

In this problem we have

`csc(x)=(13)/(5)`

substitute

`(13)/(5)=(1)/(sin(x))`

solve for sin(x)

`sin(x)=(5)/(13)`

`cos^(2)(x)+sin^(2)(x)=1`

substitute the value of sin(x) and solve for cos(x)

`cos^(2)(x)+((5)/(13))^(2)=1`

`cos^(2)(x)=1-((5)/(13))^(2)`

`cos^(2)(x)=((13^(2)-5^(2))/(13^(2)))`

`cos^(2)(x)=((144)/(13^(2)))`

`cos^(2)(x)=((12^(2))/(13^(2)))`

`cos(x)=((12)/(13))`

The function tangent is equal to

`tan(x)=(sin(x))/(cos(x))`

substitute the values

`tan(x)=((5/13))/((12/13))=5/12`