Answer to Question #306567 in Trigonometry for yen

Question

Find the quadrant in which 𝑃(𝑡) lies if 𝑠𝑒𝑐 𝑡 > 0 and 𝑐𝑠𝑐 𝑡 < 0.

Answer 1

csc t = 1/sin t

 

sec t = 1/ cos t

From the above illustration;

sin t < 0 in the 3^rd and 4^th Quadrant

and cos t >0 in the 1^st and 4^th 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 4^th Quadrant [Answer]