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Generate a Sine Wave Graph from a Circle - Trigonometry Help - Game Tips: - Get 4 correct answers and spin the ferris wheel ! - When you ride a ferris wheel, your vertical positions compared to the centre of the wheel form a sine wave pattern based on the rotation angle of the ferris wheel. - The equation y = A sin(T) represents a set of ordered pairs of the form (T,y) with y representing vertical height and T representing the angle of rotation. - When graphed on a horizontal T-axis and vertical y-axis, the curve represented by y = A sin(T) is a sine wave having vertical amplitude = |A| and horizontal wavelength = 2(Pi). - In the ferris wheel example, A is the maximum vertical distance above the centre of the wheel. The amplitude of the wave is based on the radius of the ferris wheel. In this game r=1 unit. - Wavelength refers to how long it takes for a pattern to repeat itself. Eg. a crest + a trough . The wavelength of the wave is based on one complete wheel rotation = 360 degrees. - A rotation of 360 degrees is also described in Math as an angle of 2(Pi) radians. This means that one wavelength of y = A sin(T) is approximately 2(3.14159) = 6.3 units long. [Radian measure can be based on a circle's Circumference = 2(Pi)r, where Pi=3.14159 approx.] - The basic sine wave y= sin(T) has amplitude 1 unit and an approximate wavelength of 6.3 units. - It may take a minute to load the game at dial-up speeds. - The game can be played using the mouse by itself or using the keyboard by itself. - If the game doesn't respond to keyboard input, click inside the game area to reset the game's focus. - Adjust the game's speed by pressing the + or - key repeatedly. |
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