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How To Find the Vertex of a Parabola

find vertex of parabola: Graph of a quadratic equation

To find the vertex of a parabola, you first need to know how to graph quadratic equations. When graphing these, remember that every quadratic function can be put into a standard form (more on this later). This allows you to find the leading coefficient and solve for the x-intercepts. The x-intercept and y-intercept are points on the graph where the parabola intersects the x-axis or y-axis.

Putting the quadratic function into standard form will also let you find the axis of symmetry, the line that runs through the vertex and divides the parabola in half. You can then find the x-coordinate and y-coordinate of the vertex, which is the highest or lowest point on a parabola.

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Sine Function, Cosine Function, and Tangent Function Explained

Sine function in a right triangle

There are three basic functions to understand in trigonometry: sine function, cosine function, and tangent function. Each function takes in an angle measure, which is called theta and represented by the symbol sine function: symbol θ. The angle measure is usually expressed in radians or degrees. The output of the function is a ratio comparing one side of the triangle to another.

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How To Find the Length of a Triangle

how to find the length of a triangle: Example of the Law of Sines in action

You’ll be asked how to find the length of a triangle over and over again in math and trigonometry. Maybe you need to find the missing side of a right triangle, maybe you know both side b and side c, or maybe you know only the opposite angle of the length of a side you are trying to find. In any case, we have formulas to help.

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How To Find the Third Side of a Triangle in 3 Ways

how to find the third side of a triangle: graph of the law of sines

There are several different ways you can compute the length of the third side of a triangle. Depending on whether you need to know how to find the third side of a triangle on an isosceles triangle or a right triangle, or if you have two sides or two known angles, this article will review the formulas that you need to know.

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What Is the Domain of Tangent, Sine, and Cosine?

domain of tangent: graph of three reciprocal functions

The main three trigonometric functions are the sine function, cosine function, and tangent function, sometimes represented as sin x, cos x, and tan x. These functions measure the ratio between different sides of a triangle. The easiest way to memorize these trigonometric functions is the mnemonic device SOHCAHTOA:

Sine = Opposite over Hypotenuse

Cosine = Adjacent over Hypotenuse

Tan = Opposite over Adjacent

Understanding tangent, sine, and cosine as functions enables us to figure out the range and domain of tangent, sine, and cosine.

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