find the amplitude and period of:
2 cos4x + 5 sin4x
To find the amplitude and period of the given function:
Amplitude:
The amplitude of a function can be found by looking at the coefficients of the cosine and sine functions. In this case, the coefficient of the cosine function is 2, and the coefficient of the sine function is 5. The amplitude is determined by the larger of these two coefficients, which is 5. Therefore, the amplitude of the given function is 5.
Period:
The period of a function can be calculated using the formula T = 2π/|B|, where B is the coefficient of x in the trigonometric function. In this case, the coefficient of x for both the cosine and sine functions is 4. Calculating the period using the formula, we have T = 2π/4, which simplifies to π/2. Therefore, the period of the given function is π/2.
In summary:
Amplitude = 5
Period = π/2