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Math Help - Deriving trigonmetric identities, little confused?

  1. #1
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    Deriving trigonmetric identities, little confused?

    I was reading through a text book on trigometric identities and gave the definition:
    • cos(a) = sin(a + 90) // (1a)
    • sin(a) = cos(a - 90) // (2a)

    then it went to derive another two new identities from the above identities
    • cos(a) = -sin(a-90) // (1b)
    • sin(a) = -cos(a+90) // (2b)


    What I don't understand is steps involved from deriving (1a) to (1b) and (2a) to (2b), any help would be appreciated
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  2. #2
    Senior Member MaxJasper's Avatar
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    Re: Deriving trigonmetric identities, little confused?

    Draw a circle and show sin & cos axes on it and relevant angles...then all will be clear.
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    Re: Deriving trigonmetric identities, little confused?

    Thank you for your reply, although specifically I wanted to see how you could derive the identities algebraically. That is, cos(a) = sin(a + 90) to cos(a) = -sin(a-90) and similalrly for the other identity. If you could show the steps, that would be great
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  4. #4
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Deriving trigonmetric identities, little confused?

    \cos (\alpha -90)=\sin (90) \sin (\alpha )+\cos (90) \cos (\alpha )
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