You need to find the solutions to the given equation `cos 5x=1` , over the interval `[0^o,360^o]` such that:

`cos 5x = 1 => 5x = arccos 1 => x = (arccos 1)/5`

Since the value of cosine function is equal to 1 at `x = 0^o` or `x= 360^o` ,...

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You need to find the solutions to the given equation `cos 5x=1` , over the interval `[0^o,360^o]` such that:

`cos 5x = 1 => 5x = arccos 1 => x = (arccos 1)/5`

Since the value of cosine function is equal to 1 at `x = 0^o` or `x= 360^o` , hence, the solutions to the given equation are the followings, such that:

`x = 0^o/5 => x = 0^o`

`x = 360^o/5 => x = 72^o`

**Hence, evaluating the solutions to the given equation, over the interval `[0^o,360^o],` yields `x = 0^o` and `x = 72^o` .**