When |B| is larger than one, the new period is smaller than the original, so the function will appear horizontally compressed. By altering the value of B (the multiplier of the variable before the function is evaluated), we can change the period of the function according to the formula sin(x), cos(x), sec(x), and csc(x) all have a period of \(2\pi\), while tan(x) and cot(x) have a period of \(\pi\). The period of any trig function is the length of one cycle. Note that a negative value of A will flip the graph of any function across the \(x\)-axis. The other trig functions (tangent, cotangent, secant, and cosecant) do not have an amplitude, but multiplication by A will affect their steepness. We can change the amplitude of these functions by multiplying the function by a constant A. The amplitude of a sinusoidal trig function (sine or cosine) is it's 'height,' the distance from the average value of the curve to its maximum (or minimum) value. The graphs of the six basic trigonometric functions can be transformed by adjusting their amplitude, period, phase shift, and vertical shift. Use the slider to zoom in or out on the graph, and drag to reposition. The original base function will be drawn in grey, and the transformation in blue. Choose a base trigonometric function, then change its amplitude, period, phase shift, and vertical shift using the inputs.
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