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At the point (8,4). The line )A is inclined at an angle p radians to the x axis.

(a) find the exact values of
(i) sin(2p)
(ii) cos(2p)

The line OB is inclined at an angle 2p radians to the x axis
(b) wtie down the exact value of gradient OB.
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dvs
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(a)
(i)
sinp = 4/sqrt[8²+4²] = 2/sqrt[20]
cosp = 8/sqrt[8²+4²] = 4/sqrt[20]
sin(2pi) = 2sinpcosp = (2*2*4)/20 = 0.8

(ii)
cos(2p) = 1 - 2sin²(p) = 1 - 2(0.2) = 0.6

(b)
gradient of OB = tan(2p) = sin(2p)/cos(2p) = 0.8/0.6 = 4/3

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