The given function is y=35cos(12x−π4) y = \frac{3}{5} \cos \left( \frac{1}{2} x - \frac{\pi}{4} \right) y=53cos(21x−4π). The basic function here is y=cos(x) y = \cos(x) y=cos(x).
Combine the identified transformations to understand the overall effect on the basic cosine function:
The function y=35cos(12x−π4) y = \frac{3}{5} \cos \left( \frac{1}{2} x - \frac{\pi}{4} \right) y=53cos(21x−4π) is a vertically compressed cosine function with an amplitude of 35\frac{3}{5}53, horizontally stretched by a factor of 2, and shifted to the right by π4\frac{\pi}{4}4π.
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