Question

The correct answer in each box. spell all words correctly

Answer 1

The question can be expressed diagrammatically as

where

`y=\frac{\sqrt[]{7}}{3}`

To find x, we can consider the triangle;

Using the Pythagorean Theorem, we have

`\begin{gathered} 1^2=(\frac{\sqrt[]{7}}{3})^2+x^2 \\ 1=(7)/(9)+x^2 \\ x^2=1-(7)/(9)=(2)/(9) \\ x=\frac{\sqrt[]{2}}{3} \end{gathered}`

Next, we bring out the Trigonometric ratios:

`\begin{gathered} \sin \theta=\frac{\sqrt[]{7}}{3} \\ \cos \theta=\frac{\sqrt[]{2}}{3} \\ \tan \theta=\frac{\sqrt[]{7}}{3}/\frac{\sqrt[]{2}}{3}=\sqrt[]{(7)/(2)} \end{gathered}`

Therefore,

`\frac{3}{\sqrt[]{7}}=(1)/(\sin\theta)=co\sec \theta`

and

`\sqrt[]{(7)/(2)}=\tan \theta`