What is the reciprocal of sin θ?

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cosine θ

sinθ

cosecθ

tanθ

answer is C.

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Detailed Solution

We have to find the reciprocal of sin θ.
In a right-angled triangle, the sin θ is given as the ratio between the opposite side and the hypotenuse.
Diagram

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Diagram

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sinθ = \frac{Opposite side}{hypotenuse}

Taking the reciprocal,

\frac{1}{sinθ} = \frac{1}{\frac{Opposite side}{hypotenuse}}

\frac{1}{sinθ} = \frac{hypotenuse}{Opposite side}

Now,

cosecθ = \frac{hypotenuse}{Opposite side}

So,

\frac{1}{sinθ} = cosecθ

Thus, the reciprocal of sin θ is cosec θ.
Hence, option 3 is correct.

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