In what interval(s) between 0 and 2π are tanθ and cosθ both negative?

Question

Please walk me through each step and why. It would be greatly appreciated.

Answer 1

Have you heard of the following saying? All Students Take Calculus

It corresponds to which trig functions are positive in which quadrants.

Q1 - A (All a positive)

Q2 - S (Sin is positive)

Q3 - T (Tan is positive)

Q4 - C (Cos is positive)

Tan and cos are both negative in Q2, where sin is the only function that is positive.

Q2 would be π/2 to π.