"use the composite argument property to write y=4 cos (x-35*) as a linear combination of cos x and sin x" ?

Posted on November 5, 2009 by admin

My teacher gave me this problem and the answer, but I do not understand how the process to get to the answer.

my best guess is to use the angle difference formula for cos:
cos (a – b) = cos a cos b + sin a sin b

so cos (x – 35) = cos x cos 35 + sin x sin 35

and 4cos (x – 35) = 4[cos x cos 35 + sin x sin 35]

here, we can find values for cos 35 and sin 35 to plug in, leaving only the linear combination of cos x and sin x

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One Response to "use the composite argument property to write y=4 cos (x-35*) as a linear combination of cos x and sin x" ?

  1. notthejake says:
    November 5, 2009 at 8:31 am

    my best guess is to use the angle difference formula for cos:
    cos (a – b) = cos a cos b + sin a sin b

    so cos (x – 35) = cos x cos 35 + sin x sin 35

    and 4cos (x – 35) = 4[cos x cos 35 + sin x sin 35]

    here, we can find values for cos 35 and sin 35 to plug in, leaving only the linear combination of cos x and sin x
    References :