How do I get my display from my 13 inch Macbook Air to show fully on my tv?

So I was looking forward to having my tv as a bigger monitor for my mac, but it doesn't show the display fully on the tv. It'll have some black cut edges to where I can't see the top menu bar, and can only see half of the icons on the bottom bar. How do I fix this problem? (I'm using a small tv by the way) I'm getting sound and a nice picture on the tv, but it's just not showing the entire screen on there. I'm connecting my mac to the tv using a Thunderbolt to HDMI adaptor I bought off Amazon. Thanks!