Fundamental trignometry problem

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SUMMARY

The sine function, denoted as sin(θ), is defined as the ratio of the length of the leg opposite angle θ to the length of the hypotenuse in a right triangle. This definition is established to facilitate the solution of various practical problems involving right triangles. The clarity of this definition is crucial for understanding trigonometric ratios and their applications in mathematics and engineering.

PREREQUISITES
  • Understanding of right triangles and their properties
  • Basic knowledge of trigonometric functions
  • Familiarity with angle measurement in degrees or radians
  • Concept of ratios and proportions
NEXT STEPS
  • Study the unit circle and its relationship to trigonometric functions
  • Learn about the Pythagorean theorem and its applications in trigonometry
  • Explore the definitions and applications of cosine and tangent functions
  • Investigate real-world applications of trigonometric ratios in fields such as physics and engineering
USEFUL FOR

Students of mathematics, educators teaching trigonometry, and professionals in fields requiring geometric calculations will benefit from this discussion.

mritunjay
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how is trignometric ratios like sine theta is defined to be the ratio of perpendicular and hypotenuse in a right angled triangle?
 
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Perhaps you need to find a better translation of your question, this does not make much sense.
 
A definition is whatever you want it to be. The standard definition of sin([itex]\theta[/itex]), where [itex]\theta[/itex] is an angle in a right triangle, is "length of the leg opposite angle [itex]\theta[/itex] divided by the length of the hypotenuse", which is, I guess, what you meant by "vertical". If you meant why it was defined that way, then the only reasonable answer is "because that definition helps to solve many practical problems involving right triangles".
 

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