Algebraic manipulation of trigonometric functions

[wild osprey]

These are two different equations.
The cosine equation has cos(-2) turn to cos(2).

The sine equation has no sign change when 4sin(5) is manipulated.

I haven't been able to find a reason why this makes sense on my own. Does it have to do with the domain or the range of trig functions? (This is my guess.)

I just need to figure out the rules to dealing with trig functions in equations.

Thank you.

[shrewd ice]

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[compact ridge]

cosine is even, meaning f(x) = f(-x)

@wild osprey

[wild osprey]

Thank you. Does this rule have a name or what would I look up to read more on it?

[languid loom]

@wild osprey has given 1 rep to @compact ridge

[wild osprey]

+close