Understanding the Question: csc^-1 (cotanΘ)

[lucifer_x]

Homework Statement

If tan^-1 (3/5) = Θ , what is csc^-1 (cotanΘ)

i don't get the question

 

[CompuChip]

Try writing everything in terms of sines and cosines.

 

[HallsofIvy]

Another way to do this is to draw a triangle. Since tangent= "opposite leg over near leg", draw a right triangle havine legs of length 3 and 4, with the leg of length 3 opposite angle $\theta$. Find the length of the hypotenuse using the the Pythagorean theorem (if it isn't obvious) and then it should be simple to find cotan($\theta$).

Another, rather obvious, way to do this is to use a calculator!

 

[03myersd]

tan^-1 (3/5) = Θ , what is csc^-1 (cotanΘ)

If tan^-1(3/5) = Θ then tan(Θ) = 3/5

csc^-1(cot(Θ)) = csc^-1(1/tan(Θ)) = csc^-1(1/3/5) = csc^-1(5/3)

You should be able to take it from there.