Question

Explain how it is possible to have sin(theta) < 0, cos(theta) < 0, and tan(theta) > 0. For which values of theta between 0 and 2????
does this happen?

Answer 1

Answer:

π < ∅ < 3π/2

Step-by-step explanation:

Look at the unit circle. sin() and cos() are less than 0, so they are negative. The only place where cos() and sin() are both negative is in the third quadrant (the area I shaded in green).

tan() is the same as sin()/cos(). If you look in the third quadrant, you can divide the sin() value by the cos() at any point and it'll give you a positive number between 0 and 2 because negative divided by negative will give you a positive number.