solve exactly over the indicated interval: cot(theta)=0, all real numbers
if cotØ =0
then tanØ is undefined
and we know that the tangent is undefined at π/2 and 3π/2
solve over the indicated interval expressed in degrees to 2 decimal places. sec(theta/2)=1.4275, 0<theta<360degrees
To solve the equation cot(theta) = 0, where theta represents all real numbers, we need to find the values of theta that make the cotangent function equal to zero.
The cotangent function is defined as cot(theta) = 1/tan(theta). So, to find the values for theta where cot(theta) = 0, we can set the denominator, tan(theta), equal to zero.
The tangent function, tan(theta), is equal to zero at certain angles. Specifically, it is zero at angles where the sine function, sin(theta), is zero.
The sine function is zero at angles where theta is an integer multiple of pi. In other words, theta = n * pi, where n represents any integer.
Now, substituting the values of theta into the cotangent function, we get cot(n * pi) = 0.
Since the cotangent function repeats every pi radians, the solution is a set of infinite solutions for theta. It can be written as:
theta = n * pi, where n represents any integer.
Therefore, the solution to cot(theta) = 0, for all real numbers theta, is theta = n * pi, where n is an integer.