Read the following statements carefully and answer the questions that follow:
A student claims, “Because sinθ is always less than or equal to 1 for an acute angle θ, the value of cscθ must always be greater than or equal to 1.”
(i) Explain, with reason, whether the student’s claim is correct.
(ii) Using similar reasoning, explain why secθ cannot take a value between −1 and 1 for any acute angle θ.
(iii) If tanθ increases, describe qualitatively how cotθ changes. Give a brief justification based on the definition of these ratios.