2019年4月27日 · Taking the simplest case, [MATH]y = \sin(bx)[/MATH], notice that the start of one cycle of the sine is when the argument [MATH]bx = 0[/MATH], and the end is when [MATH]bx = 2\pi[/MATH]. Those are, respectively, [MATH]x=0[/MATH] and [MATH]x=\frac{2\pi}{b}[/MATH]. That is why the period is [MATH]\frac{2\pi}{b}[/MATH].

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2022年6月21日 · The value of b determines both the period and frequency, but neither are equal to b. In a standard, non-transformed sine or cosine function, the period is 2pi (or 360 if you're working in degrees), because in that case b=1. If b has a different value for a specific function, that will affect the value of both the period and frequency.

2014年12月1日 · It works for everything except $\tan$ and $\cot$. $\tan$ and $\cot$ themselves have period $\pi$, not $2 \pi$, so the period of $\tan(bx)$ is $\frac{\pi}{b}$, not $\frac{2 \pi}{b}$.

2020年5月10日 · Most places just tell you the formula: period = 2pi/B, and then leave it at that. I would like to know why it actually works. Edit: The way I tried to understand it is, 2pi is the amount of time (suppose seconds) it takes for a traditional …

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2019年12月19日 · To begin with both degrees and radians are a measure of angle. So 2Pi = 360 degrees, which is one full rotation starting from a vector pointing in the + direction along the x-axis and then going ccw around once through all four quadrants. The confusing part is …

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Detailed step by step solution for (2pi)/b =pi. Solutions. Integral Calculator Derivative Calculator Algebra Calculator Matrix Calculator More... Graphing. Line Graph Calculator Exponential Graph Calculator Quadratic Graph Calculator Sin graph Calculator More... Calculators.

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why use 2pi/b to find period of sine/cosine. Here’s the best way to solve it. This AI-generated tip is based on Chegg's full solution. Sign up to see more! Review the standard periods for the sine, cosine, tangent, and cotangent functions: sine and cosine have a period of 2 π, while tangent and cotangent have a period of π.

What is the answer to (2pi)/b = pi/2 ?

2013年8月21日 · You might think it sounds backwards to divide 2pi by B when it is a multiplying factor in the equation y=Asin(Bx), but by doing this we travel twice the distance in the same space. In 2pi units, we travel through 2 cycles of sine, and two cycles of the circle.

2023年1月31日 · Calculate B, the find the period = 2pi/B. in the given graph D = 0. A = 2. C = maybe 0.25 or so. B =2pi/3. period = 2pi/B = 3. period looks like 3. I'll help you understand math! The period is the distance between two repeating points on the graph. The easiest places to check are at the highest or lowest points. How far is it from (-2,2) to (1,2)?

Solve the equation for b b. Tap for more steps... Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.

From all of these graphs, it is easy to see that the b value affects the period of the cosine function as well. In fact it takes 1/b times to complete a period of a curve. If b is equal to 1, then it takes 2pi to complete a period. If b is equal to 2, then it takes only pi to complete a period.

2016年9月9日 · Period = (2pi)/B = (2pi)/1 = 2pi Phase shift = C/B = pi/1=pi to the right. A negative sign in the parentheses means shift right. To graph, one complete sine curve must be 2pi "wide" because the period is 2pi. And, a phase shift of pi to the right means the beginning of the sine curve should start at pi. Also, note the negative in front of the sin.

How do you write the equation of the cosine function with an amplitude of 1/2, a period of 2pi, and a phase shift of 3pi/2?

In general, the period of `y=sin bx` is `(2pi)/|b|`, and the period of `y=cosbx` is `(2pi)/|b|`. Since the period is the length of an interval, it must always be a positive number. Since it is possible for `b` to be a negative number, we must use `|b|` in the formula to be sure the period, `(2pi)/|b|`, is always a positive number.

In celebration of `\pi` Day, approximate `\pi` using a fun (but inefficient) method known as "Buffon's Needle."