When students graph trigonometric functions, they often make some common mistakes. Here are a few of them:
Not Understanding Amplitude: Some students forget that amplitude changes how tall the waves are. For example, in the equation (y = 2\sin(x)), the amplitude is 2. This means the waves go 2 units up and down from the center, not just 1 unit.
Ignoring Periodicity: Students might miss the period of the wave. This can lead to drawing the waves too close or too far apart. For example, in (y = \cos(2x)), the period is (\frac{2\pi}{2} = \pi). This means the wave finishes one full cycle in (\pi) units.
Mistaking the Phase Shift: If students miscalculate the phase shift, the shape of the graph can look wrong. For example, in (y = \sin(x - \frac{\pi}{2})), the graph shifts to the right by (\frac{\pi}{2}).
By avoiding these mistakes, your graphs will look clearer and be easier to understand!
When students graph trigonometric functions, they often make some common mistakes. Here are a few of them:
Not Understanding Amplitude: Some students forget that amplitude changes how tall the waves are. For example, in the equation (y = 2\sin(x)), the amplitude is 2. This means the waves go 2 units up and down from the center, not just 1 unit.
Ignoring Periodicity: Students might miss the period of the wave. This can lead to drawing the waves too close or too far apart. For example, in (y = \cos(2x)), the period is (\frac{2\pi}{2} = \pi). This means the wave finishes one full cycle in (\pi) units.
Mistaking the Phase Shift: If students miscalculate the phase shift, the shape of the graph can look wrong. For example, in (y = \sin(x - \frac{\pi}{2})), the graph shifts to the right by (\frac{\pi}{2}).
By avoiding these mistakes, your graphs will look clearer and be easier to understand!