Additional Maths Trigonometry Graph

• Nathpoop

  1 Sep 09, 17:37

  I have completely no idea how to draw trigo fnc graphs in spite of my teacher's guidelines, someone help please, 1st attempt of trigo graphs.

  For each of the following expressions, state the amplitude and period of y, and sketch (on separate diagrams) its graph for the given interval

  (a) y = 3 cos 2x + 2 for 0deg=<x<=360deg

  MANY THANKS :D

• wee_ws

  1 Sep 09, 17:54

  Hi,

    Follow these transformations:

    1. Sketch y = cos x. It has amplitude 1 and period 2 pi.

    2. Sketch y = cos 2x, which is a horizontal stretch of factor 1/2. It has amplitude 1 and period pi.

    3. Sketch y = 3 cos 2x, which is a vertical stretch of factor 3. It has amplitude 3 and period pi.

    4. Sketch y = 3 cos 2x + 2, which is a shift of 2 units upward. It has amplitude 3 and period pi.

    Thanks!

  Cheers,
  Wen Shih

• Nathpoop

  1 Sep 09, 18:48

  Originally posted by wee_ws:

  Hi,

    Follow these transformations:

    1. Sketch y = cos x. It has amplitude 1 and period 2 pi.

    2. Sketch y = cos 2x, which is a horizontal stretch of factor 1/2. It has amplitude 1 and period pi.

    3. Sketch y = 3 cos 2x, which is a vertical stretch of factor 3. It has amplitude 3 and period pi.

    4. Sketch y = 3 cos 2x + 2, which is a shift of 2 units upward. It has amplitude 3 and period pi.

    Thanks!

  Cheers,
  Wen Shih

  Thanks! I'm able to solve it now.

  Now i have another question:

  From y = 5 + sin 2x,  the period i calculated is 2pi / 2 = pi = 180deg but the answer for the period is 2/pi that is 90deg. Why is that so?

  And From y = 6cos(x/2) - 4, the period stated is 4pi, how do i arrive to 4pi?

  Thanks in adv once again.

• Ajimal

  1 Sep 09, 21:50

  y = 6cos(x/2) - 4

  Look at cos(x/2). cos(x/2) means that only half of the curve will be completed from 0° to 360°.

  To complete the other half of the curve, u need another 360° more. Therefore, the curve will be completed at 360+360=720°. Thus, the period for cos(x/2) is 720° or 4π.

  However, i dun understand why the period for y = 5 + sin 2x is 90°. Its suppose to be 180°, I tink.

  Keep in mind that im juz a student. Soo my explaining and my answers might be wrong.