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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.
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.
Therefore the period of this function is equal to 2 /6 or /3. To find the phase shift, take -C/B, or - /6. Another way to find this same value is to set the inside of the parenthesis equal to 0, then solve for x.
2 maj 2022 · For the exercises 1-8, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes. 1) \(f(x)=-3\cos x+3\) Answer. amplitude: \(3\); period: \(2\pi \); midline: \(y=3\); no asymptotes. 2) \(f(x)=\dfrac{1}{4}\sin x\) 3) \(f(x)=3\cos\left ( x+\dfrac{\pi }{6} \right )\) Answer
The period of this graph is one-third of \(360^{\circ}\), or \(120^{\circ}\). The graphs in the previous example illustrate a general rule about sine and cosine graphs. Amplitude, Period, and Midline.
Given a Generalized Sine/Cosine Curve: Find Amplitude, Period, and Phase Shift Example. State the amplitude, period, and phase shift of $\,y = 5\sin(3x-1)\,.$ Solution
