Question

If cos X = -1/2, where X lies in 3rd quadrant , Find value of remaining trigonometric functions​

Answer 1

Step-by-step explanation:

cosx=−

2

1

∴secx=

cosx

1

=−2

Now ∵sin

2

x+cos

2

x=1

⟹sin

2

x=1−cos

2

x⟹sin

2

x=1−

4

1

=

4

3

⟹sinx=±

2

3

Since x lies in third quadrant, the value of sinx will be negative.

∴sinx=−

2

3

cscx=

sinx

1

=−

3

2

tanx=

cosx

sinx

=

(−

2

1

)

(−

2

3

)

=

3

cotx=

tanx

1

=

3

1