What is the period of the tangent function? The period is π
What do the vertical lines at - 1.5, 1.5, 4.7 etc represent? The vertical lines are asymptotes.
These lines cannot be crossed and hence as the angle approaches those values the graph of the tangent function will go ± ∞
Why can't these asymptote be crossed?
What are these numbers converted to degrees? -1.57, 1.57, 4.71 ≈ -90o, 90o, 270o
The tan θ = opposite side/adjacent side as the angle θ → 90o the adjacent side → goes to zero.
This means we are trying to divide the length(which is a number) of the opposite side by zero and
in our mathematical system we cannot divide by zero so the tangent function has vertical asymptotes
at whatever angles make the adjacent side zero.
Take five minutes and try to think of what other trig functions have vertical asymptotes and at what angles?
To help answer the question draw a right triangle and try to determine if the adjacent or opposite side become zero
as the angle changes and they are the denominator.
Which of the remaing trig functions will not intersect the x axis? Why? next
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