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# If Cot θ = 40 9 , Find the Values of Cosecθ and Sinθ. - Geometry

ConceptApplication of Trigonometry

#### Question

If $\cot\theta = \frac{40}{9}$, find the values of cosecθ and sinθ.

#### Solution

We have,

${cosec}^2 \theta = 1 + \cot^2 \theta$

$\Rightarrow {cosec}^2 \theta = 1 + \left( \frac{40}{9} \right)^2$

$\Rightarrow {cosec}^2 \theta = 1 + \frac{1600}{81} = \frac{1681}{81}$

$\Rightarrow cosec \theta = \sqrt{\frac{1681}{81}} = \frac{41}{9}$
Now,
$\sin\theta = \frac{1}{cosec\theta}$
$\Rightarrow \sin\theta = \frac{1}{\frac{41}{9}}$
$\Rightarrow \sin\theta = \frac{9}{41}$
Thus, the values of cosecθ and sinθ are $\frac{41}{9}$ and $\frac{9}{41}$, respectively.

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#### APPEARS IN

Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 6: Trigonometry
Practice set 6.1 | Q: 3 | Page no. 131
Solution If Cot θ = 40 9 , Find the Values of Cosecθ and Sinθ. Concept: Application of Trigonometry.
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