Find the sign for the following.

Question

Number 10 is the one I need help with most. I don't know how to determine the sign and would like an explanation of how to do it in order to prepare for my future exams and quizzes.

Thank You In Advance:)

Answer 1

9) sec(-θ)=sec(θ) because cos(-θ)=cos(θ). But θ is in Q3 where cos is negative so the sign is A) negative.

10) cot(θ+180) has the same sign as tan(θ+180)=tan(θ), which is negative because θ is in Q4 where tan(θ) is negative. So A) negative.

11) cos(θ+180)=-cos(θ). When θ is in Q2 cos(θ) is negative. So negative negative makes positive and in this case the answer is A) positive.