Question

Can I get some help on this i got stuck

Answer 1

Given:

Given that

$\tan\theta=\sqrt{5}$

Required:

To find the other five trig ratio.

Explanation:

$\begin{gathered} \tan\theta=\frac{opp}{adj} \\ \\ =\frac{\sqrt{5}}{1} \end{gathered}$

Now the hypotenuse is,

$\begin{gathered} hyp^2=opp^2+adj^2 \\ \\ hyp^2=5+1 \\ \\ =5+1 \\ \\ =6 \\ \\ hyp=\sqrt{6} \end{gathered}$

Now,

$\begin{gathered} \sin\theta=\frac{opp}{hyp} \\ \\ =\frac{\sqrt{5}}{\sqrt{6}} \end{gathered}$$\begin{gathered} \cos\theta=\frac{adj}{hyp} \\ \\ =\frac{1}{\sqrt{6}} \end{gathered}$$\begin{gathered} cot\theta=\frac{adj}{opp} \\ \\ =\frac{1}{\sqrt{5}} \end{gathered}$$\begin{gathered} sec\theta=\frac{hyp}{adj} \\ \\ =\frac{\sqrt{6}}{1} \end{gathered}$$\begin{gathered} cosec\theta=\frac{hyp}{opp} \\ \\ =\frac{\sqrt{6}}{\sqrt{5}} \end{gathered}$

Final Answer:

The six trig ratio are

$\begin{gathered} \sin\theta=\sqrt{\frac{5}{6}} \\ \cos\theta=\frac{1}{\sqrt{6}} \\ cot\theta=\frac{1}{\sqrt{5}} \\ sec\theta=\sqrt{6} \\ cosec\theta=\frac{\sqrt{6}}{\sqrt{5}} \end{gathered}$