Pre-Cal

Find sin 2x, cos 2x, and tan 2x from the given information.

[1]. sin x = 8/17, x in Quadrant I

1). sin 2x =________.

2). cos 2x =________.

3). tan 2x =________.

[2]. sin x = -5/13, x in Quadrant III

1). sin 2x =________.

2). cos 2x =________.

3). tan 2x =________.

[Note: I'm having a lot of trouble with these. From what I'm told the answers are suppose to come in fraction forms]

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  3. 👁 3,796
  1. sinx = 8/17
    so, cosx = 15/7

    sin2x = 2 sinx cosx = 2 * 8/7 * 15/7 = 240/49

    do the others similarly.

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    2. 👎 2
  2. oops

    sinx = 8/17
    so, cosx = 15/17

    sin2x = 2 sinx cosx = 2 * 8/17 * 15/17 = 240/289

    1. 👍 5
    2. 👎 1
  3. I will do the 2nd one, which is the harder of the two.
    Follow my steps to do the first one.

    sinx = -5/13 ,and the angle x is in III
    recall that sinØ = y/r
    so y = -5, r = 13
    sketch a right-angled triangle in III with hypotenuse 13 and y = -5
    x^2 + y^2 = r^2
    x^2 + 25 =169
    x^2 = 144
    x = ± 12 , but we are in III, so x = -12

    giving us cosx = -12/13

    recall that sin 2x = 2sinx cosx
    = 2(-5/13)(-12/13)
    = 120/169

    recall cos 2x = cos^2 x - sin^2 x
    = 144/169 - 25/169
    = 119/169

    recall tan 2x = sin2x/cos2x
    = (120/169) / (119/169)
    = 120/119

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