Question

If sin 0= - 3/5 and 180°< 0 < 270° then tan o=​

Answer 1

Answer:

3/4

Step-by-step explanation:

Correct Question :-

If sinθ = -3/5 and 180°< θ < 270° then tanθ = ?

Given,

sinθ = -3/5

180°< θ < 270°

To Find :-

Value of tanθ.

Solution :-

As :- 180°< θ < 270°

→  θ is in 3rd quadrant.

In 3rd quadrant "sin" is negative and "tan" is positive.

So the value of tanθ should be positive.

$sin\theta=\dfrac{opposite\:side}{hypotenuse}$

$\implies \dfrac{-3}{5}=\dfrac{opposite\:side}{hypotenuse}$

→ 3 = opposite side[ As sin is negative we should not consider its sign]

5 = hypotenuse

Applying pythagoras theorem :-

$(5)^2=(3)^2+(adjacent\:side)^2$

$25 = 9 + adjacent \:side^2$

$adjacent\:side^2=16$

Adjacent side = 4

$\implies tan\theta=\dfrac{opposite\:side}{adjacent\:side}$

$=\dfrac{3}{4}$

tanθ  = 3/4

Know More :-

Trigonometric ratios

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj