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2 answers:
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Answer:
a. Cosine is an even function
b. Sine is an odd function
c. cos(x) = sin(x + pi/2)
Step-by-step explanation:
See the plot attached.
a. In the figure it can be seen that, for example, cos(pi/2) = cos(-pi/2); therefore, cosine is even.
b. In the figure it can be seen that, for example, sin(pi/2) = 1; sin(-pi/2) = -1; therefore, sine is odd.
c. Function displacements along x-axis are made adding (or subtracting) values to x; i. e., f(x + a), where a is a constant, displace the function f(x) a steps to the left. It can be seen in the figure that sine is cosine but displaced pi/2 values to the right. So, sin(x + pi/2) will displace sine pi/2 values to the left, where cosine is placed.
