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# Trig - Co-function identities watch

1. I know these co-function identities from my notes:

cos(0.5pi - x) = sin(x)
sin(0.5pi - x) = cos(x)

However In an excercise that I'm doing, it would be useful to have some variations of these. What would the corresponding identities of the above be for +x instead of -x? And what about if it was (x-0.5pi) instead?

I think I've managed to work some of them out but could someone confirm if they are indeed true for all values of x?

I get:

cos(0.5pi + x) = -sin(x)
sin(0.5pi + x) = cos(x)
sin(x - 0.5pi) = ?
cos(x - 0.5pi) = ?
2. (Original post by nugiboy)
cos(0.5pi + x) = -sin(x)
sin(0.5pi + x) = cos(x)
sin(x - 0.5pi) = ?
cos(x - 0.5pi) = ?
The first two are right. For the second two, let . Then you're trying to find and , which you should know how to express in terms of and . But we know that and , so you can work out what they are.
3. (Original post by nugiboy)
I know these co-function identities from my notes:

cos(0.5pi - x) = sin(x)
sin(0.5pi - x) = cos(x)

However In an excercise that I'm doing, it would be useful to have some variations of these. What would the corresponding identities of the above be for +x instead of -x? And what about if it was (x-0.5pi) instead?

I think I've managed to work some of them out but could someone confirm if they are indeed true for all values of x?

I get:

cos(0.5pi + x) = -sin(x)
sin(0.5pi + x) = cos(x)
sin(x - 0.5pi) = ?
cos(x - 0.5pi) = ?
The first two you've found are right. For the other two, do you know what the definition of an even or odd function is? If so, is an odd function and is an even function i.e. and . Now notice that .

EDIT: nuodai is just too quick.
4. ahh that makes sense i think!

Would they be:

sin(x - 0.5pi) = -sin(0.5pi - x) = -cos(x)
cos(x - 0.5pi) = cos(0.5pi - x) = sin(x)
5. (Original post by nugiboy)
ahh that makes sense i think!

Would they be:

sin(x - 0.5pi) = -sin(0.5pi - x) = -cos(x)
cos(x - 0.5pi) = cos(0.5pi - x) = sin(x)
Yep.
6. Thanks guys

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