Name three values of theta that would result in y equal to cot times theta being undefined.
any even multiple of 180°
since cotθ = cosθ/sinθ, wherever sinθ = 0 the fraction will be undefined.
fyi: cot(theta) is read "cotangent of theta". It is not a product, but a function
To find the values of theta that would make y = cot(theta) undefined, we need to consider the properties of the cotangent function.
The cotangent function is defined as the ratio between the adjacent side and the opposite side of a right triangle. It is equal to the cosine of the angle divided by the sine of the angle. Mathematically, cot(theta) = cos(theta) / sin(theta).
Since the cotangent function is undefined when the sine of theta equals 0, we need to identify the values of theta that make sin(theta) equal to 0.
In the unit circle, the sine function equals 0 at every multiple of pi (π), where n is an integer. So, the values of theta that would make y = cot(theta) undefined are:
1. theta = n * pi, where n is an integer
2. theta = 0 (since sin(0) = 0)
Therefore, we have three values of theta that would result in y = cot(theta) being undefined: theta = 0, theta = pi, and theta = -pi.