Questions: Identify the quadrant for the angle θ satisfying the following conditions. cos(θ)<0 and csc(θ)<0 A. Quadrant IV B. Quadrant II C. Quadrant I D. Quadrant III

Solution Steps

• In Quadrant I, all trigonometric functions are positive.
• In Quadrant II, $\sin$ and $\csc$ are positive; $\cos$, $\sec$, $ an$, and $\cot$ are negative.
• In Quadrant III, $ an$ and $\cot$ are positive; $\sin$, $\csc$, $\cos$, and $\sec$ are negative.
• In Quadrant IV, $\cos$ and $\sec$ are positive; $\sin$, $\csc$, $ an$, and $\cot$ are negative.

• Condition 1: $cos \theta < 0$ implies Quadrants 2, 3.
• Condition 2: $csc \theta < 0$ implies Quadrants 3, 4.

Final Answer: