State the period in radians for each of the following functions
A) y=cosx
B) y=sin2x
C) y=tan3x
D) y=cos(x/2)
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Sure! To determine the period in radians for each of the given functions, we need to look at the coefficient of x within each function.
A) For the function y = cos(x), there is no coefficient of x. In this case, the period is determined by the general form of the cosine function, which is 2π. Therefore, the period for y = cos(x) is 2π.
B) For the function y = sin(2x), the coefficient of x is 2. To find the period, we divide 2π (the general period of the sine function) by the coefficient of x. In this case, the period is 2π/2 = π. So, the period for y = sin(2x) is π.
C) For the function y = tan(3x), the coefficient of x is 3. Similar to the previous case, we divide 2π by the coefficient of x. Hence, the period for y = tan(3x) is 2π/3.
D) For the function y = cos(x/2), the coefficient of x is 1/2. Again, dividing 2π by the coefficient gives us the period: 2π / (1/2) = 4π. Thus, the period for y = cos(x/2) is 4π.
So, to summarize:
A) Period of y = cos(x) is 2π.
B) Period of y = sin(2x) is π.
C) Period of y = tan(3x) is 2π/3.
D) Period of y = cos(x/2) is 4π.