Vertical asymptotes?
Which of the following functions have a vertical asymptote for values of theta such that cos theta =1?
y=sin theta
y=cos theta
y=tan theta
y=sec theta
y=csc theta
y=cot theta
Update:I think it is y=csc theta and y=cot theta...
Which of the following functions have a vertical asymptote for values of theta such that cos theta =1?
y=sin theta
y=cos theta
y=tan theta
y=sec theta
y=csc theta
y=cot theta
Update:I think it is y=csc theta and y=cot theta...
Comments
You are correct.
When cos(theta) = 1, sin(theta) = 0.
tan(theta) = sin(theta) / cos(theta) = 0/1 = 0. But cot(theta) = cos(theta) / sin(theta) = 1/0 = undefined. Vertical asymptote here.
sec(theta) = 1 / cos(theta) = 1/1 = 1. But csc(theta) = 1 / sin(theta) = 1/0 = undefined. Vertical asymptote here.
You are correct.
sin theta = 0 when cos theta = 1 (or -1), so any ratio with sine "on the bottom" is undefined. Those are cot theta = (cos theta)/(sin theta); and csc theta = 1/(sin theta).