Read the following statements carefully and answer the questions that follow:
A student claims, “Because $
sin \thetaisalwayslessthanorequalto1foranacuteangle
\theta,thevalueof
\csc \theta$ must always be greater than or equal to 1.”
a. (i) Explain, with reason, whether the student’s claim is correct.
b. (ii) Using similar reasoning, explain why $
\sec \thetacannottakeavaluebetween-1and1foranyacuteangle
\theta$.
c. (iii) If $
\tan \thetaincreases,describequalitativelyhow
\cot \theta$ changes. Give a brief justification based on the definition of these ratios.