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.