Find the quadrant in which 𝑃(𝑡) lies if 𝑠𝑒𝑐 𝑡 > 0 and 𝑐𝑠𝑐 𝑡 < 0.
csc t = 1/sin t
sec t = 1/ cos t
From the above illustration;
sin t < 0 in the 3rd and 4th Quadrant
and cos t >0 in the 1st and 4th Quadrant.
Therefore,
When sec t > 0 ▶ cos t > 0
and when csc t <0 ▶ sin t < 0
𝑃(𝑡) lies in the quadrant on which the two relations overlap each other
hence,
𝑃(𝑡) is in the 4th Quadrant [Answer]
Comments