from the intervals 0 less than or equal to theda less than 2 pie, what is cot theda of 2
Do you want the angle whose cotangent is 2? That would be written
cot^-1 2
It is the same as the angle(s) with tangent 1/2.
Since you want it in radians, it is 0.4636 radians in the first quadrant of pi plus that number in the third quadrant.
To find the value of cot(theta) at theta = 2, we need to first determine the value of cot(theta) and then substitute theta = 2 into the equation.
Cotangent is the reciprocal of the tangent function, so we can find cot(theta) using the tangent function:
cot(theta) = 1 / tan(theta)
Since we are given the interval 0 <= theta < 2π, the value of cot(theta) can be determined by finding the value of tan(theta).
Next, we substitute theta = 2 into the equation to find the value of cot(2):
cot(2) = 1 / tan(2)
Now, we need to compute the value of tan(2). Let's go step by step:
1. Convert 2 degrees to radians by multiplying it with π/180:
2 * π/180 = π/90 radians
2. Use the tangent function to find tan(π/90):
tan(π/90) ≈ 0.01745506493
Finally, we substitute tan(2) into the equation for cot(2):
cot(2) ≈ 1 / 0.01745506493
Using a calculator, we find:
cot(2) ≈ 57.2909245739
Therefore, cot(2) is approximately 57.2909245739.