What are the x intercepts of a cosine graph?
The x-intercepts are locations on the coordinate plane where the y-value of the ordered pair is 0. The cosine function evaluates to 0 at the following values (nπ2,0) where n is odd integer.
Do cosine graphs have amplitude?
Amplitude and Period a Cosine Function The amplitude of the graph of y=acos(bx) is the amount by which it varies above and below the x -axis. The period of a cosine function is the length of the shortest interval on the x -axis over which the graph repeats.
What is the y-intercept of the cosine graph?
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The y-intercept is the point where the graph of the function crosses the y-axis. The point lies on the y-axis. The y-intercept of the above graph can be found by substituting the value of x as zero. ∴ The y-intercept of the graph y=cosx is 1.
How do you write a period with amplitude and cosine?
1 Answer
- In y=acos(b(x−c))+d :
- • |a| is the amplitude. • 2πb is the period.
- The amplitude is 3 , so a=3 .
- The period is 2π3 , so we solve for b .
- b=3.
- The phase shift is +π9 , so c=π9 .
- The vertical transformation is +4 , so d=4 .
- ∴ The equation is y=3cos(3(x−π9))+4 , which can be written as y=3cos(3x−π3)+4.
What is amplitude in sin and cosine?
The amplitude of the sine and cosine functions is the vertical distance between the sinusoidal axis and the maximum or minimum value of the function. In relation to sound waves, amplitude is a measure of how loud something is.
How do you find the amplitude of a trig function?
The amplitude of a trigonometric function is half the distance from the highest point of the curve to the bottom point of the curve: (Amplitude) = (Maximum) – (minimum) 2 . \text{(Amplitude)} = \frac{ \text{(Maximum) – (minimum)} }{2}. (Amplitude)=2(Maximum) – (minimum).
What is the amplitude of a graph?
The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine.