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March 29, 2017

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If sin(x) = /45 and cos(y) = 5/13 with both x and y terminating in quadrant 1 find the exact value of cos(x-y)

cos(4/5 - 5/13)

Is this what I would do?

  • math - ,

    Your sin(x) fraction lacks a numerator

  • math - ,

    the sine is 4/5 sorry!

  • math - ,

    No, that is not what you would do. Call the angles A and B.

    For the angles you have chosen,
    cos(x) = 3/5 and sin(y) = 12/13. You can prove that with the Pythagorean theorem, or sin^2 + cos^2 = 1. That will make the calculation easier.

    Then use the identity:

    cos(A-B) = cosA cosB + sinA sin B
    = (3/5)(5/13) + (4/5)(12/13)
    = (15 + 48)/65 = 63/65

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