Question

Csc θ given that sin θ= √11/6I have added an example.

Answer 1

Given that

`\sin \theta=\frac{\sqrt[]{11}}{6}`

Required: Value of csc θ

Solution:

Step 1:

From the reciprocal trigonometric identities,

`\csc \theta=(1)/(\sin\theta)\text{ ----- equation 1}`

where

`\sin \theta=\frac{\sqrt[]{11}}{6}`

Step 2:

Substitute the value of sin θ into equation 1.

Thus,

`\begin{gathered} \csc \theta=(1)/(\sin\theta) \\ \csc \theta=\frac{1}{\frac{\sqrt[]{11}}{6}}=\frac{6}{\sqrt[]{11}} \end{gathered}`

Step 3:

Rationalize the surd obtained in step 2.

Thus, we have

`\begin{gathered} \csc \theta=\frac{6}{\sqrt[]{11}} \\ \text{Multiply the numerator and denominator by }\sqrt[]{11.} \\ \text{thus,} \\ \Rightarrow\frac{6}{\sqrt[]{11}}*\frac{\sqrt[]{11}}{\sqrt[]{11}} \\ =\frac{6\sqrt[]{11}}{11} \end{gathered}`

Hence, the value of csc θ is evaluated to be

`\frac{6\sqrt[]{11}}{11}`