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3 years ago

How do I graph a function based off the unit circle?

1 answer:

7 0

So if you remember what the normal y = sin(x) function looks like (a wave), y = 2 sin(4x) is just changed a little.

The standard format for sine/cosine function
y = a sin(bx− c) + d

a = amplitude, distance from center of the wave to the highest point. This function a = 2 so the height of the sine wave reaches 2 instead of 1.
"c" and "d" shift the graph left/right and up/down respectively. These equal zero so the sine wave is not shifted.

The range (y-values) is then just the amplitude -2 ≤ y ≤ 2

The domain (x-value) is all real numbers because the wave just keeps going on to infinity in both directions.

2π / |b| = period, distance per wave
this equation b = 4
period is then π/2
this is the distance before a wave repeats.

Graph
 x | y
-π/8 -2
 0 0
π/8 2
3π/8 -2
5π/8 2

see the pattern? I'm using the amplitude or peaks and bottoms of the wave y = 2 and -2 then using the x-distance between like points is the period so you add π/2

(π/8 , 2)
+ π/2
(5π/8 , 2)

Same for the minumums of the wave (y = -2)
(-π/8 , -2)
+ π/2
(3π/8 , -2)

Hope this helps, otherwise there are youtube videos you can watch or try an online graphing calculator like Desmos.com

You might be interested in

Cual es la diferencia entre divisor y divisible

Anna [14]

La diferencia entre divisor y divisible es que los números compuestos (número que posee más de dos divisores) son los divisores y los números divisible son los números enteros como el 10,15,20,25 y 30.

espero que esto ayude

7 0

2 years ago

Which statement best explains the relationship between

-Dominant- [34]

Answer: They are not perpendicular because their slopes are not negative reciprocals.

Step-by-step explanation:

For these two lines to be perpendicular, their slopes have to be negative reciprocals.

Slope of FG.

F = (-4, 1)

G = (0, -2)

= (Y₂ - Y₁) / (X₂ - X₁)

= (-2 - 1) / (0 + 4)

= -3/4

Slope of HJ

J = (0 , 4)

H = (-4, -2)

Slope = (Y₂ - Y₁) / (X₂ - X₁)

= (-2 - 4) / (-4 -0)

= 6/4

= 3/2

The slopes of these lines are not negative reciprocals so these lines are not perpendicular.

4 0

3 years ago

In the function f(x)=(x-2)^2+4, the minimum value occurs when x is

Vinil7 [7]

The graph of the function is a parabola.

The nose comes down as far as y=4 but no farther.

That happens when (x - 2)² = 0 , and THAT happens when x = 2 .

6 0

3 years ago

Read 2 more answers

Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your

Veronika [31]

The expression of integral as a limit of Riemann sums of given integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ is 4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$ from i=1 to i=n.

Given an integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ .

We are required to express the integral as a limit of Riemann sums.

An integral basically assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinite data.

A Riemann sum is basically a certain kind of approximation of an integral by a finite sum.

Using Riemann sums, we have :

$\int\limits^b_a {f(x)} \, dx$ = $\lim_{n \to \infty}$ ∑f(a+iΔx)Δx ,here Δx=(b-a)/n

$\int\limits^5_1 {x/(2+x^{3}) } \, dx$ =f(x)= $x/2+x^{3}$

⇒Δx=(5-1)/n=4/n

f(a+iΔx)=f(1+4i/n)

f(1+4i/n)= $[n^{2}(n+4i)]/2n^{3}+(n+4i)^{3}$

$\lim_{n \to \infty}$ ∑f(a+iΔx)Δx=

$\lim_{n \to \infty}$ ∑ $n^{2}(n+4i)/2n^{3}+(n+4i)^{3}4/n$

=4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$

Hence the expression of integral as a limit of Riemann sums of given integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ is 4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$ from i=1 to i=n.

Learn more about integral at brainly.com/question/27419605

#SPJ4

5 0

1 year ago

2+3x<8;2 check whether the given number is a solution of the equation or inequality

Phoenix [80]

Answer:

equation is the answer.

3 0

2 years ago