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Period: π 3, Frequency: 6. Explanation: Our equation is in the form y = A ⋅ sin(fx − h) + k. where A is the amplitude, f is the frequency, h is the horizontal shift, and k is the vertical shift. We can look at the equation and see that the frequency, f, is 6. The period is 2π f, so in this case 2π 6 = π 3.
Precalculus. Trigonometry. Find Amplitude, Period, and Phase Shift. y = 2cos (4x − π 4) y = 2 cos (4 x - π 4) Use the form acos(bx−c)+ d a cos (b x - c) + d to find the variables used to find the amplitude, period, phase shift, and vertical shift. a = 2 a = 2. b = 4 b = 4.
2 maj 2022 · For the exercises 1-4, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes. 1) \(f(x)=\tan x-4\) Answer. stretching factor: none; period: \(\pi \); midline: \(y=-4\); asymptotes: \(x=\dfrac{\pi }{2}+\pi k\), where \(k\) is an integer
Period, Midline and Amplitude. All sine and cosine graphs have the characteristic ”wave” shape we’ve seen in previous examples. But we can alter the size and frequency of the waves by changing the formula for the function. In the next example we consider three variations of the sine function.
For the equations y = A sin(Bx + C) + D, amplitude is |A| period is 2 /|B| phase shift is -C/B; vertical shift is D; In our equation, A=-1, B=1, C=-, and D=3. Next, apply the above numbers to find amplitude, period, phase shift, and vertical shift. To find amplitude, look at the coefficient in front of the sine function.
We can have all of them in one equation: y = A sin(B(x + C)) + D. amplitude is A; period is 2 π /B; phase shift is C (positive is to the left) vertical shift is D; And here is how it looks on a graph: Note that we are using radians here, not degrees, and there are 2 π radians in a full rotation.
In the next section, you will write an equation of a curve with a specified amplitude, period, and phase shift. Sample question: Write an equation of a sine curve with amplitude $\,5\,,$ period $\,3\,,$ and phase shift $\,2\,.$
