Question

if sin thita =3/5 then the value of cosec thita is​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{sin\,\theta=\dfrac{3}{5}}$

$\underline{\textbf{To find:}}$

$\textsf{The value of}\;\mathsf{cosec\,\theta}$

$\underline{\textbf{Solution:}}$

$\mathsf{We know that,}$

$\mathsf{cosec\,\theta\;is\;reciprocal\;of\;sin\,\theta}$

$\mathsf{cosec\,\theta=\dfrac{1}{sin\,\theta}}$

$\mathsf{cosec\,\theta=\dfrac{1}{\dfrac{3}{5}}}$

$\implies\boxed{\mathsf{cosec\,\theta=\dfrac{5}{3}}}$

Answer 2

Given,

sinθ = $\frac{3}{5}$.

To Find,

The value of cosecθ.

Solution,

We can solve this numerical problem using the process as follows-

We know that the ratio of the length of the opposing side to the length of the hypotenuse is equal to the sin theta(θ) of a right-angled triangle.

We also know that, cosecθ is just the reciprocal of sinθ.

This means,

sinθ×cosecθ=1.

⇒cosecθ = $\frac{1}{sin (theta)}$.

⇒cosecθ = $\frac{1}{\frac{3}{5} } =\frac{5}{3}$.

Hence, the value of cosecθ is $\frac{5}{3}$ .