Find the exact values of the vertical asymptotes for o is less than or equal to Q is less than or equal to pi for the function y= cot(3Q)
I need to show my work for this one but I do not know how to do this.
To find the vertical asymptotes of the function y = cot(3Q), we need to determine the values of Q where the function goes to positive or negative infinity.
A vertical asymptote occurs when the function approaches infinity or negative infinity as the independent variable, in this case, Q, approaches a certain value.
The cotangent function is defined as cot(Q) = cos(Q) / sin(Q). The cotangent function has vertical asymptotes where sin(Q) equals zero, since dividing by zero is undefined.
To find the values of Q for which sin(Q) equals zero, we need to solve the equation sin(Q) = 0.
The sine function is equal to zero at integer multiples of pi. Therefore, we can write the equation as:
sin(Q) = 0
Q = n * pi
where n is an integer.
Now, let's find the values of Q between o and pi where we have vertical asymptotes.
When n = 0, Q = 0 * pi = 0
When n = 1, Q = 1 * pi = pi
Therefore, the values of Q between o and pi where we have vertical asymptotes are Q = 0 and Q = pi.
To summarize, the exact values of the vertical asymptotes for 0 ≤ Q ≤ π for the function y = cot(3Q) are at Q = 0 and Q = π.