Question

If the angle alpha in the third quadrant and tan alpha=2, then sin alpha is equal to​

Answer 1

Answer:

2/ root5

Step-by-step explanation:

As we know

tan alpha = p/b

2=sin alpha/ cos alpha

therefore applying pythagoras theorum

2^2 + 1^2 = h^2

h = root 5

sin alpha = -2/ root 5 since tan theta lies in 3rd quadrant

hence (B) is the answer

Answer 2

Answer:

The value of sin α = - $\frac{2}{\sqrt{5} }$

Step-by-step explanation:

Given,

The angle 'α' is in the third quadrant

tanα = 2

To find,

value of sinα

Recall the concepts

In the third quadrant, the value of sin is negative

Cot α = $\frac{1}{tan \alpha}$

cosec²  α = 1+Cot² α

Sinα  = $\frac{1}{cosec \alpha}$

Solution

Cot α = $\frac{1}{tan \alpha}$ = $\frac{1}{2}$

cosec² α = 1+Cot² α = 1+( $\frac{1}{2}$)² = 1+$\frac{1}{4}$ = $\frac{5}{4}$

cosec² α =$\frac{5}{4}$

sin² α = $\frac{1}{cosec^2 \alpha}$ = $\frac{4}{5}$

sin  α = $\sqrt{\frac{4}{5}}$ =± $\frac{2}{\sqrt{5} }$

The value of sin  α = - $\frac{2}{\sqrt{5} }$(since the value of sin is negative in the third quadrant)

∴sin α = - $\frac{2}{\sqrt{5} }$

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