Question

Cot x =3/4,x lies in third quadrant

Answer 1

By pythagoras theorem

OP²=MP²+OM²

OP²=(4)²+(3)²

OP²=16+9

OP²=25

OP²=+_5

Op=-5

then,

Sinx=-4/5

Cosx=-3/5

Tanx=4/3

Cosecx=-5/4

Secx=-5/3

Answer 2

Answer:

X lies in third quadrant sin and Cos will be positive

Step-by-step explanation:

Given: cot x=3/4

we know that

1+cot²x=cosec²x

1+(3/4)²=cosec²x

1+9/16=cosec²x

taking lcm

16+9/16=cosec²x

25/16=cosec²x

cosec²x=+_5/4

X is in third quadrant sin x is negative in third quadrant cos x is negative in third quadrant

cosecx=-5/4

sin x= 1/cosec x

1/-5/4=

-4/5

tan x= 1/cot x

1/3/4=

4/3

tan x= sin x/ cos x

cos x= sin x/ tan x

-4/5×3/4

4 and 4 is cancel out

then cos x= -3/5

sec x= 1/ cos x

= 1/-3/5=

=-5/3

TRIGONOMETRY RATIO ARE

sin x= -5/4

tan x= 4/3

cos x= -3/5

sec x=-5/3

cosec x= -5/4

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