Trigonometric of tangent and sine functions

In summary, the tangent and sine functions are both trigonometric functions used to calculate ratios in right triangles. The tangent function is the ratio of the opposite side to the adjacent side, while the sine function is the ratio of the opposite side to the hypotenuse. These functions have various real-world applications and can be graphed on a coordinate plane. They also have special properties and can be solved using trigonometric identities and the unit circle.
  • #1
anemone
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MHB
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Simplify $\left(\tan \dfrac{2\pi}{7}-4\sin \dfrac{\pi}{7}\right)\left(\tan \dfrac{3\pi}{7}-4\sin \dfrac{2\pi}{7}\right)\left(\tan \dfrac{6\pi}{7}-4\sin \dfrac{3\pi}{7}\right)$.
 
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  • #2
I got about -8.7083121069873265814843145114959219999438416220762493062309701968483080116471438626714199913273209202440106287205185869613863265722279384849632901398226721432702744787955199077781973792055631357781755415456733331388124469116498805756011983384506433640247288593850820089590928253650738597742412754348439402301589178427587352708579714081417809559865987679591010005488147679340458470850085945675037017144904042287279335497160556553452963874716319026939725908000014025345344112227718546669183167834689374961602264946845122520973969612465747159538537772604016219227651262298967156522926816165972425283143645081705710618441263404832174787619393871431981552587401078586609898568054592224581007986448669288148444215128498186229896741206349315952054866256984612864167199842472866575465952447085845790874114020207148838309575537421068097653460699858226519033408205869208586639796284569971790165922274544500088737294024496093237634962135759638417523292668843921768916664652250085254395250841082981914897137469833874653795905403859395226103590166597307639852476273392879083873723649605334228340639098097814440444549718831560592044450598723461692804007733588937741590648889021935199757480637837660523461803937847078950866107512314217003731198786042996011750451712135884514444878781114357178952544416819768594073353584110967734337432198244086867356343864416552649586451520413569547092694404444532795994994438271445333716459116502792251091594744077024600155160457563503684373664211499889132746530159707148096441069149624420565803877227318131627873671715105932608979648146278844613590157353436714676787933231516958800501704045205913556958442328349254532043183475963879427381686337157339601066369199608533673687386762949721994907024739645071023865884051877078161059364899178505753714909479228031574944638783941268199880771092085126999780242627307210910698666574484989827761671955524479251591513340499083326461726929118742316319408632872884749801756534634165971359295929387392681708974873301182019170001880197471302122860499952496977...

Am I close?

-Dan
 

What is the definition of a tangent function?

A tangent function is a mathematical function that describes the relationship between the opposite and adjacent sides of a right triangle. It is defined as the ratio of the length of the opposite side to the length of the adjacent side.

What is the definition of a sine function?

A sine function is a mathematical function that describes the relationship between the opposite and hypotenuse sides of a right triangle. It is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

What is the period of a tangent function?

The period of a tangent function is π radians, or 180 degrees. This means that the graph of the function repeats itself every π radians or 180 degrees.

What is the period of a sine function?

The period of a sine function is 2π radians, or 360 degrees. This means that the graph of the function repeats itself every 2π radians or 360 degrees.

What are the key properties of tangent and sine functions?

The key properties of tangent and sine functions include periodicity, symmetry, and amplitude. Both functions have a repeating pattern, are symmetric about the origin, and have a maximum amplitude of 1.

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