How do I make the camera look at the player while rotating?

I have recreated the wiki code to help explain how CFrames work. This is my base example which is a local script in StarterCharacterScripts.

-- sevices
local runServ = game:GetService("RunService")
local camera = workspace.CurrentCamera

-- player root part
local rootPart = script.Parent:WaitForChild("HumanoidRootPart")

local offsetCFrame = CFrame.new(0, 10, 30) -- reuse this value
while true do
	for i=1, 360 do
		
		-- Example using wiki code
		-- start camera at the players position
		local tmpCF = CFrame.new(rootPart.Position)
		
		-- angle the CFrame 
		-- angles are in radians so convert degrees ->  radians	
		tmpCF = tmpCF * CFrame.Angles(0, math.rad(i), 0) 
			
		-- offset to worlds pace ie add 10y and 30z to the look vector
		tmpCF = tmpCF * offsetCFrame
	
		camera.CFrame = tmpCF
											
		runServ.RenderStepped:Wait() -- wait one frame before creating the next CFrame
	end
end

The steps take in this code for the camera are:-

• Start at player Vector3
• Rotate to the CFrame by the current degrees
• Offset to world space

As this is the end position you can create a new CFrame using the constructor CFrame.new(position Vector3, lookAt Vector3) if you wanted to make a CFrame looking back at the player.

-- sevices
local runServ = game:GetService("RunService")
local camera = workspace.CurrentCamera

-- player root part
local rootPart = script.Parent:WaitForChild("HumanoidRootPart")

local offsetCFrame = CFrame.new(0, 10, 30) -- reuse this value
while true do
	for i=1, 360 do
		
		-- Example using wiki code
		-- start camera at the players position
		local tmpCF = CFrame.new(rootPart.Position)
		
		-- angle the CFrame 
		-- angles are in radians so convert degrees ->  radians	
		tmpCF = tmpCF * CFrame.Angles(0, math.rad(i), 0) 
			
		-- offset to worldspace ie add 10y and 30z to the look vector
		tmpCF = tmpCF * offsetCFrame
	
		-- create a new CFrame from the end position looking at the player
		camera.CFrame = CFrame.new(tmpCF.p, rootPart.Position)
											
		runServ.RenderStepped:Wait() -- wait one frame before creating the next CFrame
	end
end

Some maths fun using sin :3

-- sevices
local runServ = game:GetService("RunService")
local camera = workspace.CurrentCamera

-- player root part
local rootPart = script.Parent:WaitForChild("HumanoidRootPart")

local offsetCFrame = CFrame.new(0, 10, 30) -- reuse this value
while true do
	for i=1, 360 do
		
		-- Example using wiki code
		-- start camera at the players position
		local tmpCF = CFrame.new(rootPart.Position)
		
		-- angle the CFrame 
		-- angles are in radians so convert degrees ->  radians	
		tmpCF = tmpCF * CFrame.Angles(0, math.rad(i), 0) 
			
		-- offset to worldspace ie add 10y and 30z to the look vector
		-- use sine for height also needs radians
		tmpCF = tmpCF * CFrame.new(0, (math.sin(math.rad(i))) * 2 + 2, 30)
	
		camera.CFrame = CFrame.new(tmpCF.p, rootPart.Position)
											
		runServ.RenderStepped:Wait() -- wait one frame before creating the next CFrame
	end
end

I hope this helps