Question

Find the other trigonometric functions if If cot x=3/4,x lies in the third quadrant​

Answer 1

cotx = 3/4

tanx = 1/cotx = 4/3

cosec²x -cot²x = 1

cosec²x = 1+(3/4)² =1+9/16 = 16+9/16 = 25/16

cosec²x = 25/16

cosecx = 5/4

in third quadrant cosecx will be negative = -5/4

sinx = 1/cosecx = - 4/5

sin²x+ cos²x = 1

(-4/5)² + cos²x = 1

cos²x = 1-(16/25) = 25-16/25 = 9/25

cos²x = 9/25

cosx= 3/5

in third quadrant cosx willbe negative = -3/4

secx= 1/cosx = -4/3