Angle theta lies in quadrant 2. Without using a calculator, determine if the following ratios are true or false. Explain your reasoning.

Question

Angle  lies in quadrant 2. Without using a calculator, determine if the following ratios are true or false.  Explain your reasoning.

a) 

b) 

Answer 1

b is false. All cosecants of any angle in any quadrant, is never between -1 and +1

csc(theta) cannot = -0.542

a tangents in quadrant 2 are always negative and can be any real number, from negative to positive infinity. tan(theta) = -1.323 is a possible ratio for opposite side over adjacent side, where adjacent side <0 and < oppositie side. tangents of angles are the opposite side over the adjacent side.