Question

Find the period of cos4x+9/5

Answer 1

Answer:

The period of the function cos[(4x+9)/5 is 5π/2.

Step-by-step explanation:

Transformation Theory:

• The period of a function y = f(x) differs if and only if a constant is multiplied to the input.
• That is, the period of the transformed function y = a + f(bx + c) + d, will change only because of the factor 'b', additions/subtractions of the factors 'a,c and d' won't affect the period of the function in any way.
• And, the new period of the transformed function will be P/b, if P was the initial period.

Further math:

The function cos(4x/5+9/5) is a transformation of the original function cos(x) and as discussed above, the period will differ only because of the multiplication factor '4/5'.

Since, the period of the original function (cosx) is 2π, the period of the function cos(4x/5+9/5) will be 2π/(4/5) = 10π/4 = 5π/2.

Anternative way - Graph plotting:

• Plot the graph for the function, y = cos(4x/5 + 9/5).
• Determine two consecutive points, equal in magnitude on the y-axis.
• Mark and subtract their respective x-values to get the period of the transformed function.

Here, the two consecutive x-values for which the function outputs the same magnitude(i.e., 1) is 3π and π/2.

Thus, it's period = 3π - π/2 = (6π-π)/2 = 5π/2.