18.0K
MAAn easy way to graph a function y=kx²
1. Shifting ✔️
2. Dilation ✔️
3. Reflecting ✔️
4. Shifting + Dilation ✔️
5. Shifting + Dilation + Rotation ✔️
#math
#mathematics
#matematik
#function
@mathteacherziya
#Sinh Function Graph
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SCYou guys were right, my original sine graph looked like a cubic. So I deleted, beat myself up for a couple days and tried again. Hopefully this sine graph transformation is better.
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KISine function graph❤️❤️
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PHLet’s explore the relationship between the unit circle and the sine function!
As we move along the arc of the unit circle, starting at coordinate (1,0), our x and y positions change.
Sin(θ) can be thought of as the y coordinate as we move along the unit circle. The point moves around the circle, generating a real-time graph of sin(θ).
Dash lines connect the circle to the graph, highlighting the movement in the Cartesian plane.
Updated values of sin(θ) and the angle theta in degrees are displayed dynamically.
Visualize trigonometry in a unique way!
🔥 Follow 👉 @physic.fun
Cre: @fourierborel
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YOGraph 📉 of some common mathematical functions
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MAFunction transformations allow us to modify the appearance of a function while keeping its fundamental structure intact. These transformations include shifts, reflections, stretches, and compressions. Vertical transformations affect the output (y-values), such as multiplying a function by a constant to change its amplitude. Horizontal transformations, on the other hand, involve changes to the input (x-values), which can stretch or compress the function along the x-axis. Understanding these transformations is essential for analyzing functions, as they help us predict how a graph changes when we manipulate its equation.
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MATrigonometry becomes much clearer when we connect algebraic formulas to geometry. This visual explanation starts with the unit circle, a circle of radius 1 centered at the origin, which forms the foundation of trigonometric definitions. Any angle measured from the positive x-axis determines a point on the unit circle, and the coordinates of this point directly define cosine and sine. The x-coordinate represents cos θ, while the y-coordinate represents sin θ.
By dropping a perpendicular from this point to the x-axis, we naturally obtain a right-angled triangle. This links the unit circle to the familiar concepts of adjacent, opposite, and hypotenuse. From this construction, tan θ appears as the ratio of sine to cosine and is visualized using the tangent line to the unit circle.
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MAVisualizing the Graph of SinX and inverse SinX
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MAIn this short, we show five different graphs of functions with a point where the function is not differentiable.
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To learn more about animating with manim, check out:
https://manim.community
@mathvisualproofs
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