Question

If sine= 2/3, which of the following are possible for the same value of ?

Answer 1

Given

`\sin\theta=(2)/(3)`

Find

which of the following are possible?

Step-by-step explanation

as we know ,

`\begin{gathered} \sin\theta=(P)/(H) \\ \end{gathered}`

so , H = 3 , P = 2

then

`\begin{gathered} B=√(H^2-P^2) \\ B=√(9-4) \\ B=√(5) \end{gathered}`

so ,

`\begin{gathered} \cos\theta=(B)/(H)=(√(5))/(3) \\ \\ \tan\theta=(P)/(B)=(2)/(√(5)) \\ \\ sec\theta=(1)/(\cos\theta)=(3)/(√(5)) \end{gathered}`

Final Answer

Hence , the correct options are B and C