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trig

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tan(theta)=(7/24), sin(theta)<0
find cos(2theta)

  • trig - ,

    If tan is positive and sin is negative, theta is in the third quadrant. From Pythagorean considerations, sin theta = -7/25 and cos theta = -24/25. (Imagine a 7,25,25 right triangle)

    Use the double angle formula for
    cos(2 theta)
    = cos^2(theta) - sin^2(theta)
    = (24^2-7^2)/25^2 = 527/625
    2theta will be in the first quadrant, 32.5 degrees

    Check: theta = 180 + 16.26 = 196.26 deg
    2 theta = 392.50 => 32.5 degrees

  • trig (correction) - ,

    Change the third sentence to:
    (Imagine a 7,24,25 right triangle)

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