If csc x = 5/3 and sec x = 5/4, find the value of cot x.

Question

Cot x= ?  (In Fraction Form) Thanks!

Answer 1

i assume you know that cot = cos/sin.

 

And you probably know csc = 1/sin, and Sec = 1/cos.

 

so all you have to do is manipulate csc and sec into a form that equals cos/sin, then fill in the numbers.

Answer 2

csc(x) = 5/3 ⇒ 1/sin(x)=5/3. ⇒sin(x)=3/5

sec(x) = 5/4,  ⇒ 1/cos(x)=5/4 ⇒ cos(x)=4/5

 

cot(x)=cos(x)/sin(x) = (4/5)*(5/3)=4/3