Find sin 2x, cos 2x, and tan 2x from the given information. sinx=(5/13), x is in Quadrant I

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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Given, sin x = 5/13

Using the identity: sin^2 x + cos^2 x =1,

cos x = sqrt(1-sin^2 x) = sqrt (1- (5/13)^1) = sqrt (144/169) = 12/13

Using the identities:

1) sin 2x = 2 sinx cosx = 2 * 5/13 *12/13 = 120/169

2) cos 2x = 1-2sin^2 x = 1- 2*5/13*5/13 = 119/169

3) tan 2x = sin 2x / cos 2x = (120/169)/(119/169) = 120/119

Hope this helps.

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