Find the exact value of the following given that sec𝛼 =5 and 270°<𝛼<360°. sin𝛼/2

Question

Hello! Please can I have assistance with this problem! I am confused on where to start to what to do.

Answer 1

If secx = 5 then cosx = 1/5 This occurs at x = 78.5^o.

In the fourth quadrant, remember that cos(-x) = cos(x)

So, the negative angle is - 78.463^o and the positive angle is 281.537^o.

sec(-78.463) = 5 and sec(281.537) = 5

sin(-78.463/2) = -.632 and sin(281.537/2) = .632