inverse trig function

Question

cot^-1(0) find the value of the inverse trig

is it zero?

Answer 1

Hello Jared,

you need to remember the domain and range of cot^-1(x).

Domain: All real numbers aka -∞ to ∞

Range: 0 < y < π aka: all angles in Quadrants 1 and 2 EXCEPT 0 and 180 degrees

Now: cot^-1(0) means answering the question "what is the angle in the range of 0 < y < pi that has a cotangent equal to zero"

note that cotangent = cosine/sine

If you refer to your unit circle, you'll see that the only angle whose cosine/sine equals zero is 90 degrees aka π/2.

So: cot^-1(0) = π/2

Answer 2

cot^-1(0) is the angle whose cotangent = 0

cotangent = adjacent side over opposite side. To be zero means the adjacent side = 0. That happens when the angle = 90 + 180n degrees where n= any integer

the inverse function is never zero

it's 90 + 180n where n = any integer

or pi/2 +npi/2 where n= any integer