if tan theta=12/5. find the value of sin theta

Answers 2

Answer:

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Given:

tan θ = –12/5

Formula used:

tan θ = Perpendicular/Base

sin θ = perpendicular/hypotenuse

By Pythagoras theorem,

Hypotenuse2 = Perpendicular2 + Base2

Calculation:

The negative sign of tanθ shows that the value of θ can be in the 2nd or in the 4th quadrant

And we know that in the 2nd quadrant sinθ is +ve and in the 4th quadrant sinθ is -ve

It means the value of sinθ can be +ve or -ve

We have tanθ = –12/5

So, we can take perpendicular as 12x unit and base as 5x unit

From the figure,

(AC)2 = (AB)2 + (BC)2

⇒ (AC)2 = (12x)2 +(5x)2

⇒ (AC)2 = 144x2 + 25x2 = 169x2

⇒ Hypotenuse = √169x2 = 13x

According to the question:

sinθ = Perpendicular/Hypotenuse

⇒ 12x/13x = 12/13

From the above information,

The value of sinθ can be 12/13 or -12/13 but in the option we have only -12/13

∴ The answer is –12/13.

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