Question

Find the value of sin(2x) if cos(x) = 2/5 and x is between 270 and 360degrees.

Answer 1

Given

`\cos x=(2)/(5),270\degree<strong>Find</strong>[tex]\sin2x`

Step-by-step explanation

As we know that

`\sin2x=2\sin x\cos x`

and

`\cos x=(B)/(H)`

H = 5 and B = 2

By pythagoras theorem ,

`\begin{gathered} H^2-B^2=P^2 \\ 5^2-2^2=P^2 \\ 25-4=P^2 \\ P=√(21) \end{gathered}`

so ,

`\sin x=(P)/(H)=(√(21))/(5)`

as x lies in 4th quadrant , and we know sinx is negative in 4th quadrant.

so ,

`\begin{gathered} \sin2x=2\sin x\cos x \\ \sin2x=2(-(√(21))/(5))((2)/(5)) \\ \\ \sin2x=-(4√(21))/(25) \end{gathered}`

Final Answer

Hence , the correct option is 4.