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Thread: Why is cos (-θ) = cos θ?

  1. #1
    Junior Member
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    Why is cos (-θ) = cos θ?

    when the angle (say) theta is negative,

    1) sin (-θ) = - sin θ

    2. tan (-θ) = - tan -θ

    then why,

    3. cos (-θ) = cos θ? Could you explain this point here, please? I am confused.

  2. #2
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    Quote Originally Posted by Indranil View Post
    when the angle (say) theta is negative,

    1) sin (-θ) = - sin θ

    2. tan (-θ) = - tan -θ

    then why,

    3. cos (-θ) = cos θ? Could you explain this point here, please? I am confused.
    What definition have you been given for the cosine (of a non-acute angle)? We can start there.

  3. #3
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by Indranil View Post
    when the angle (say) theta is negative,

    1) sin (-θ) = - sin θ

    2. tan (-θ) = - tan -θ

    then why,

    3. cos (-θ) = cos θ? Could you explain this point here, please? I am confused.
    Think about what you learned back in algebra about even and odd functions.... (here)

  4. #4
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    Quote Originally Posted by Indranil View Post
    3. cos (-θ) = cos θ? Could you explain this point here, please? I am confused.
    For two approaches, see the unit circle here, and the graph of the cosine here.

  5. #5
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    I understand it. Thank you all.

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