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Given that tan = 7 in quadrant IV, nd sin 2, cos 2, and tan 2.
Solution
tan = 7
==> tan = 7/1
opposite side = 7 and adjacent side = 1
hypotenuse = [(-7)2 + 12] = 50
as it is in IV quadrant sine function is negative
==> hypotenuse = 52
sin 2 = 2 sin cos
==> sin 2 = 2 (-7/(52)) (1/ (52)) = -7/25
==> sin 2 = -7/25
cos 2 = cos2 - sin2
==> cos 2 =(1/ (52))2 - ( -7/(52))2 = -6/50 = -3/25
==> cos 2 = -3/25
tan 2 = sin 2 / cos 2
==> tan 2 = (-7/25)/(-3/25)
==> tan 2 = 7/3
Hence sin 2 = -7/25 , cos 2 = -3/25 , tan 2 = 7/3

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Given that tan = 7 in quadrant IV, nd sin 2, cos 2, and tan 2.S.pdf

  • 1. Given that tan = 7 in quadrant IV, nd sin 2, cos 2, and tan 2. Solution tan = 7 ==> tan = 7/1 opposite side = 7 and adjacent side = 1 hypotenuse = [(-7)2 + 12] = 50 as it is in IV quadrant sine function is negative ==> hypotenuse = 52 sin 2 = 2 sin cos ==> sin 2 = 2 (-7/(52)) (1/ (52)) = -7/25 ==> sin 2 = -7/25 cos 2 = cos2 - sin2 ==> cos 2 =(1/ (52))2 - ( -7/(52))2 = -6/50 = -3/25 ==> cos 2 = -3/25 tan 2 = sin 2 / cos 2 ==> tan 2 = (-7/25)/(-3/25) ==> tan 2 = 7/3 Hence sin 2 = -7/25 , cos 2 = -3/25 , tan 2 = 7/3