Question

If tanx= 3 and x lies in third quadrant,then the value of sinx is

Answer 1

Step-by-step explanation:

If x lies in third quadrant

we know All silver tea cups rule(ASTC)

that means tan is positive in 3rd quadrant but sin is negative in 3rd quadrant

given tanx=3/1

by trigonometry

$\tan(x) = \frac{3}{1} = \frac{opposite}{adjacent}$

$\sin(x) = \frac{opposite}{hypotenuse} = \frac{3}{ \sqrt{ {1}^{2} + {3}^{2} } }$

$\sin(x) = \frac{3}{ \sqrt{10} }$

but sin is negative in 3rd quadrant

so it is negative (