Simplifying trigonometric ratios

I'm doing a few exercises where you need to simplify trigonometric ratios of either 30, 45 to 60 degrees

Here are the examples it gave.

cos(405)
cos(405) = cos(360+45)
=cos(45)

tan(120)
tan(120) = tan(180-60)
=tan(-60)
=-tan(60)

sin(300)
sin(300)=sin(360-60)
=sin(-60)
=-sin(60)

so it seems that the rules are
sin(-x) = -sin(x), cos(-x) = -cos(x), tan(-x) = -tan(x)
sin(360+x) = sin(-360+x) = sin(x)
cos(360+x) = cos(-360+x) = cos(x)
tan(180+x) = tan(-180+x) = tan(x)

Let's say you have
cos(-210)
adding 360 won't help you in any way as you will just be left with cos(150) and the examples never bothered to show how to handle this situation. but I think you can just add or remove 180 and flip the sign

cos(-210)= -cos(-210 + 180) = -cos(-30)
= --cos(30) = cos(30), but this is wrong. So "cos(-x) = -cos(x)" does not always work. Are there any consistent rules for how to simplify these? The ones the example is showing don't even work.

I'm doing a few exercises where you need to simplify trigonometric ratios of either 30, 45 to 60 degrees

Here are the examples it gave.

cos(405)
cos(405) = cos(360+45)
=cos(45)

tan(120)
tan(120) = tan(180-60)
=tan(-60)
=-tan(60)

sin(300)
sin(300)=sin(360-60)
=sin(-60)
=-sin(60)

so it seems that the rules are
sin(-x) = -sin(x), cos(-x) = -cos(x), tan(-x) = -tan(x)
sin(360+x) = sin(-360+x) = sin(x)
cos(360+x) = cos(-360+x) = cos(x)
tan(180+x) = tan(-180+x) = tan(x)

Let's say you have
cos(-210)
adding 360 won't help you in any way as you will just be left with cos(150) and the examples never bothered to show how to handle this situation. but I think you can just add or remove 180 and flip the sign

cos(-210)= -cos(-210 + 180) = -cos(-30)
= --cos(30) = cos(30), but this is wrong. So "cos(-x) = -cos(x)" does not always work. Are there any consistent rules for how to simplify these? The ones the example is showing don't even work.