Question

find other five trigonometric functions if cot x = -3/4 lies in 4th quadrant​

Answer 1

Answer:

sin x = -(4/5)

cosec x = -(5/4)

tan x =  - (4/3)

cos x = 3/4

sec x = 4/3

Step-by-step explanation:

given cot x = -(3/4) lies in 4th quadrant, where only cos x and sec x are positive.

cot x = adj/opp = 3/4

=> tan x = opp/adj =  - (4/3)

=> opp=4 & adj=3

∴ hyp = √(opp²+adj²) = √(3²+4²) = √(9+16) = √25 = 5

=> sin x = opp/hyp = -(4/5)

   cosec x = hyp/opp = -(5/4)

   cos x = adj/hyp = 3/4

&  sec x = hyp/adj = 4/3

Answer 2

cot x= -3/4

tan x = -4/3

cosec²x -cot²x = 1

cosec² = 1 + 9/16 = 16+ 9 /16 = 25/16

cosec x = √25/16 = 5/6

(cosec x in 4th quadrant is negative )

hence cosecx = -5/6

sinx = -6/5

sin²+cos² = 1

cos² = 1-sin² = 1 - 36/25 = 25 -36/25 = -11/25

cos x = √-11/ 5 = √-11/ 5

cosx is positive in 4th quadrant