Trigonometric Equation – Tangent Formulas & Solutions :: Danielitte

Convex Quadrilateral

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Sector of Circle

Regular Poligon of N Sides

Sperical Segment

Sperical Sector

Frustum of Right Circular Cone

Triangular Prism

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Euler's Formula

Trigonometric Functions For A Right Triangle

Trigonometric Table

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Formulas With T=tan(x/2)

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Sum Of Trigonometric Functions

Product Of Trigonometric Functions

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Angles Of A Plane Triangle

Sides And Angles Of A Plane Triangle

Relationships Among Trigonometric Fuctions

Linear Equation

System of Two Linear Equation

Quadratic Equation

Exponential Equation

Logarithmic Equation

Trigonometric Equation Cos

Trigonometric Equation Sin

Trigonometric Equation Tan

Trigonometric Equation Cotan

Linear Inequation

Quadratic Inequation

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Logarithmic Inequation

Trigonometric Inequation Cos

Trigonometric Inequation Sin

Trigonometric Inequation Tan

Trigonometric Inequation Cotan

Horizontal Shifting

Vertical Shifting

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Equation of Line Joining Two Points A,B

Equation of Sphere Center at M and Radius R in Rectangular Coordinates

Equation of Ellipsoid With Center M and Semi-Axes A,B,C

Elliptic Cylinder With Axis as Z Axis

Elliptic Cone With Axis as Z Axis

Hyperboloid of One Sheets

Hyperboloid of Two Sheets

Elliptic Paraboloid

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Equations - Trigonometric Equation Tan

Trigonometric Equations: Tangent

\[ \tan x = m \]

For all real values of \( m \), the solutions are:

\[ x = \alpha + k\pi, \quad k \in \mathbb{Z} \]

where \(\alpha = \arctan m\), and \(-\frac{\pi}{2} < \alpha < \frac{\pi}{2}\).

Trigonometric Equations Tangent

Terminology

\(m\): The given real value of the tangent function.
\(\arctan m\): The inverse tangent function returning angle \(\alpha\) such that \(\tan \alpha = m\).
Periodicity: Tangent has period \(\pi\), hence the solution repeats every \(\pi\).
Parameter \(k\): An integer indicating the number of full periods added.

Applications

Used in physics for problems involving angles of elevation and depression.
Important in engineering fields like control systems and signal processing.
Used in geometry for calculating slopes of lines and inclines.
Crucial in solving integrals and differential equations with tangent functions.