Question

If cosx = 3/5 , x lies in IV quadrant, find the value of other five trigonometric functions.​

Answer 1

Answer:

Step-by-step explanation:

cosx=  

5

−3

​

 

x is in 3  

rd

 quadrant  

in 3  

rd

 quadrant only tan and cot are positive  

⟹sinx=  

5

−4

​

 

tanx=  

3

4

​

 

cotx=  

4

3

​

 

secx=  

3

−5

​

 

cscx=  

4

−5

​

Answer 2

Answer:

Since cos x = - 3/5 , we have sec x = - 5/3

Now sin2 x + cos2 x = 1, i.e., sin2 x = 1 – cos2 x

or sin2 x = 1 – 9/25 = 16/25

Hence sin x = ± 4/5

Since x lies in third quadrant, sin x is negative. Therefore

sin x = – 4/5

which also gives

cosec x = – 5/4

Further, we have

tan x = sinx/cosx = 4/3 and cot x = cosx/sinx = 3/4 .