Question

if cosec theta = 5/3 and theeta lies in quadrant 3 find the values the values of all other five trignometric functions​

Answer 1

Step-by-step explanation:

Given, sinx=

5

3

cosecx=

sinx

1

=

(

5

3

)

1

=

3

5

sin

2

x+cos

2

x=1

⇒cos

2

x=1−sin

2

x

⇒cos

2

x=1−(

5

3

)

2

⇒cos

2

x=1−

25

9

⇒cos

2

x=

25

16

⇒cosx=±

5

4

Since x lies in the 2rd quadrant, the value of cosx eill be negative

∴cosx=−

5

4

secx=

cosx

1

=

(−

5

4

)

1

=−

4

5

tanx=

cosx

sinx

=

(−

5

4

)

(

5

3

)

=−

4

3

cotx=

tanx

1

=−

3

4

.