If y = 10 - 5cos2/3x, find a) the amplitude, b) the period, c) the vertical shift, and d) the horizontal shift?
Amplitude is how magnified your function is. Is it big or small? In math terms its the coefficient of the trig function, in this case -5. The period of a trig function is 2pi. But if you put a coefficient in front of your variable this will make the number the trig function is computing grow faster or slower than your variable by itself and so the period will change. In this case the period is 3pi. Vertical shift will always be a constant in your equation that falls outside of your trig function, in this case 10. Horizontal shift will be a constant that is inside your trig function, for instance 5cos(2x + "pi/2"). This is known as a phase shift as well and for your particular equation is 0.
List the exact amplitude, period and horizontal shift for y = 2tan(pix + 3)?
amp = 2 (but it usually doesn't affect the graph of tanx or cotx) period = TT/TT = 1 horizontal shift = -3/TT (3/TT units to the left)
Find the amplitude, period, phaseshift, and vertical translation of the sinusoid y = 2 + 6 sin (3x-(pi/4)?
For starters, you have a horizontal stretch by a factor of 3 due to the coefficient 3 of x. Your phase shift is pi/4 units to the right. Amplitude is 6, vertical translation is 2. For future reference: y = a sin (bx - h) + k a is the amplitude, b is the horizontal stretching/shrinking, h is the phase shift, and k is the vertical translation. Remember to phase-shift in the opposite direction of the sign of h.
How do you find amplitude, period and horizontal shift?
Take the function "y = 2 * sin(3x - 1) + 2" for example. Remember the basic form of the equation is "y = A * sin(bx - c) + d" A = amplitude 2pi/b = period c = horizontal shift d = vertical shift So, in the example; the amplitude would be 2, the period would be 2pi/3, the horizontal shift would be 1 (to the right)
M(x) = 6 csc (pix/3 + pi) what is the period and horizontal shift?
The fundamental period of the cosecant is 2π. To get the period of your function, you have to divide this by the coefficient of x. period = 2π/(π/3) = 6. To get the horizontal shift, you need to factor our π/3 inside the cosecant. m(x) = 6 csc((π/3)(x + 3)). The graph would be shifted 3 units to the left.
What are the amplitude, period, phase shift, and midline of f(x) = -4 cos(3x - π) + 1?
f(x) = - 4 cos(3x – π) + 1 ... in this form the characteristics are: amplitude = 4 period = 2π ⁄ 3 phase shift = -π radians vertical shift = +1 average = +1 = midline ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ HOWEVER, because of the -π phase shift, this equation is equivalent to: y = 4 cos(3x) + 1 ... and in this form the characteristics are: amplitude = 4 period = 2π ⁄ 3 phase shift = 0 vertical shift = +1 average = +1 = midline
Amplitude, period, and phase shift of f(x) = 1/4cos (1/2x+pi/2)?
your basic function is y=AcosB(x-C)+D A: gives amplitude B: Affects period C: Affects Horizontal translation (or phase shift) D: affects vertical translation A normal cosine graph has an amplitude of 1 as the highest point is at 1, the lowest is at -1. Times this by your A value and you get the new amplitude for your function - in this case 1/4. It doesn't matter what the numbers in brackets are since for any cosine function where A is 1, the amplitude is 1. B is equal to 1/2 since (1/2x + pi/2) = 1/2(x+pi). This means that the period is twice that it should be (normally this is 2pi in radians or 360 degrees since that is when the curve starts repeating itself again). The period is therefore 2pi*2 = 4pi or 360*2 = 720 degrees. I guess this is a bit counter intuitive but think of it as when x= pi you get 1/4cos(pi) which is -1/4. If B=1 you would get y=1/4cos(2pi) which would equal 1. So imagine that the curve is being stretched horizontally (I know this explanation isn't very clear but am struggling to explain without visual aide) C is equal to - 1/2pi and remember that the general equation is -C so think of the equation as having a double negative to make positive: (1/2x-(-1/2pi)) which is why 1/2pi is negative) This means that the curve will be shifted horizontally by -1/2pi. There is no D value here Hopefully this made sense
Find the amplitude, period, and phase shift of the function S(x) = −2 sin 5 ( x + π/5)?
y = a sin b(x±h) ± k a : amplitude => take absolute value b : angular frequency h : horizontal shift ( phase shift). (+ left, - right) k : mid. line or vertical shift ( + up, - down) period = 2π/b ( for sines, cosines. if tangent : p = π/b) y = 2 sin (5x) http://www.wolframalpha.com/input/?i=y+%... S(x) = −2 sin 5 ( x + π/5) http://www.wolframalpha.com/input/?i=S%2...
What is the amplitude, period, domain, range and phase shift of y=-2cos (3x+pi/2) + 4 and draw the graph of the given function?
So we know that the cosine function goes from -1 to 1. Since we multiply the values of -1 to 1 by 2, 2 must be the amplitude of the function.The period is how much it takes to complete one cycle. Normally, one period is 2 pi, but for this function, there has been a stretch with a factor of 1/3 because of the 3 multiplied to the x. This means that the period is 2pi/3.The domain is the numbers in the x, and for this case the domain is all real numbers.We know that cosine can only go from -1 to 1. So the maximum value is when the cosine function is -1 and that is -2(-1)+4=6, and the minimum value is when the cosine function is 1 and that is -2(1)+4=2. That means that the range is from 2 to 6.The phase shift is whatever shift done on the x axis, so from graphical transformations we know that there is a pi/2 shift to the left.As far as plotting the graphNow you can also check the properties of the function from the graph.