csc θ = hypotenuse/opposite side
As the opposite side approaches zero the value of csc θ and hence its graph goes to ± ∞ Why?
The hypotenuse doesn't change its value (it remains constant) and the denominator (opposite side) becomes
smaller and smaller as the θ goes to zero. Hence the answer for the division of hypotenuse/opposite side becomes
larger and larger. A simple math problem illustrates this: 16/16 = 1 16/8 = 2 16/4 = 4 16/2 = 8 and so on
Explain why this graph has asymptotes? The csc θ = hypotenuse/opposite side. At the value of the asymptote the opposite side will equal zero and since we cannot divide by zero we have an asymptote.
What happens at 00, 900, 1800, 2700 and 3600 to the csc?
At 00, 1800 and 3600 the opposite side goes to zero and hence you have asymptotes.
At 900 and 2700 the opposite side and the hypotenuse become equal and hence csc θ = 1
Look at the above graph to confirm these conclusions.
return
return PCTC