Question

Hi, can you help me to solve this exercise please!!

Answer 1

It is given that

`\csc (\theta)=\frac{\sqrt[]{170}}{10}`

We know that

`\sin (\theta)=(1)/(\csc (\theta))`

`\text{Substitute }\csc (\theta)=\frac{\sqrt[]{170}}{10},\text{ we get}`

`\sin (\theta)=\frac{1}{\frac{\sqrt[]{170}}{10}}`

`\sin (\theta)=\frac{10}{\sqrt[]{170}}`
`\sin (\theta)=\frac{\sqrt[]{10}\sqrt[]{10}}{\sqrt[]{17*10}}`
`\sin (\theta)=\frac{\sqrt[]{10}}{\sqrt[]{17}}`
`\sin (\theta)=\sqrt[]{(10)/(17)}`

Hence the required value is

`\sin (\theta)=\sqrt[]{(10)/(17)}`