Question

Can I get some help on this i got stuck

Answer 1

Given:

Given that

`\tan\theta=√(5)`

Required:

To find the other five trig ratio.

Step-by-step explanation:

`\begin{gathered} \tan\theta=(opp)/(adj) \\ \\ =(√(5))/(1) \end{gathered}`

Now the hypotenuse is,

`\begin{gathered} hyp^2=opp^2+adj^2 \\ \\ hyp^2=5+1 \\ \\ =5+1 \\ \\ =6 \\ \\ hyp=√(6) \end{gathered}`

Now,

`\begin{gathered} \sin\theta=(opp)/(hyp) \\ \\ =(√(5))/(√(6)) \end{gathered}`
`\begin{gathered} \cos\theta=(adj)/(hyp) \\ \\ =(1)/(√(6)) \end{gathered}`
`\begin{gathered} cot\theta=(adj)/(opp) \\ \\ =(1)/(√(5)) \end{gathered}`
`\begin{gathered} sec\theta=(hyp)/(adj) \\ \\ =(√(6))/(1) \end{gathered}`
`\begin{gathered} cosec\theta=(hyp)/(opp) \\ \\ =(√(6))/(√(5)) \end{gathered}`

Final Answer:

The six trig ratio are

`\begin{gathered} \sin\theta=\sqrt{(5)/(6)} \\ \cos\theta=(1)/(√(6)) \\ cot\theta=(1)/(√(5)) \\ sec\theta=√(6) \\ cosec\theta=(√(6))/(√(5)) \end{gathered}`