Find the exact value of each expression.
(a) cot^-1(sqrt(3))
Steve,
Is it pi/6
that it is.
To find the exact value of the expression cot^(-1)(√3), we need to understand what cot^(-1) means.
cot^(-1) represents the inverse cotangent function or arccotangent. It is the inverse of the cotangent function cot(x). For any value of y, cot^(-1)(y) gives the angle whose cotangent is y.
Now, let's find the value of cot^(-1)(√3):
We know that cot(x) = √3 when x = π/6 (or 30 degrees) in the first quadrant because in a right-angled triangle with one angle of 30 degrees, the ratio of the adjacent side to the opposite side is √3.
So, cot^(-1)(√3) = π/6 or 30 degrees.
Therefore, the exact value of cot^(-1)(√3) is π/6 or 30 degrees.
come on. don't forget your trig now that you're taking calculus!
You surely recognize cotθ = √3
No? How about tanθ = 1/√3