Trigonometry and Its Applications

13 Questions

In trigonometry, which function is used to find the missing sides or angles of a right triangle when only two sides or one side and one angle are known?

Tangent (tan)

Which field extensively uses trigonometry to calculate the heights, distances, and angles in building construction?

Architecture

In physics, trigonometry is used to calculate which of the following?

Motion and behavior of objects

What term was first coined in 1993 to describe platforms like SixDegrees.com and LiveJournal?

Social media

What ancient writing system served as a means of communication over long distances?

Papyrus scrolls

Which platform, launched in 2003, became the first social networking site to gain widespread popularity and was used for music discovery and social networking?

MySpace

What was the main function of the telegraph invented in the 19th century?

Long-distance communication

What term refers to the way a product or service connects people and facilitates communication, collaboration, and community-building?

Social aspect

What was the initial purpose of Facebook when it was launched in 2004?

To connect Harvard students

Which social media platform became the second-largest search engine in the world?

YouTube

How many active users did Facebook have by the end of 2009?

350 million

What has been a major concern regarding the rise of social media?

Potential negative effects on mental health

What does the text suggest is essential as social media platforms continue to evolve?

Addressing concerns and ensuring positive use

Study Notes

Maths: Exploring the World of Triangles and Circles

Maths is a fascinating and diverse field that encompasses a wide range of subjects, from arithmetic and algebra to geometry and trigonometry. In this article, we will delve into the captivating world of trigonometry, a branch of mathematics that deals with the relationships between the sides and angles of triangles and the ratios of the sides of right triangles.

Triangles and Their Angles

Trigonometry is a subfield of geometry that deals with triangles and their relationships. Triangles are polygons with three sides and three angles. The sum of the angles in a triangle always equals 180 degrees. There are three types of triangles based on the lengths of their sides:

Equilateral Triangle: All three sides are of equal length.
Isosceles Triangle: Two sides are of equal length.
Scalene Triangle: All three sides are of different lengths.

Trigonometry is particularly useful in calculating the sides and angles of triangles when only two side lengths or one side and one angle are known.

Right Triangles and the Trigonometric Functions

In a right triangle, one angle is always a right angle, which measures 90 degrees. The sides of a right triangle are labeled as follows:

The side opposite the right angle is called the hypotenuse.
The two remaining sides are called the legs.

The three main trigonometric functions deal with the relationships between the sides and angles of a right triangle:

Sine (sin): The ratio of the length of the side opposite an angle to the length of the hypotenuse.
Cosine (cos): The ratio of the length of the side adjacent to an angle to the length of the hypotenuse.
Tangent (tan): The ratio of the length of the side opposite an angle to the length of the side adjacent to the angle.

These functions are often used to find the missing sides or angles of a right triangle when only two sides or one side and one angle are known.

Applications of Trigonometry

Trigonometry has a wide range of applications in various fields, including:

Architecture: Trigonometry is used in calculating heights, distances, and angles in building construction.
Navigation: Trigonometry is crucial in determining the distance and direction of objects in navigation.
Physics: Trigonometry is used in calculating the motion and behavior of objects in physics.
Astronomy: Trigonometry is essential in calculating the positions and movements of celestial bodies in astronomy.

In conclusion, trigonometry is a captivating and versatile branch of mathematics that deals with the relationships between the sides and angles of triangles. Its applications in various fields make it an essential tool for understanding and solving real-world problems. So, the next time you find yourself in a situation that requires calculating distances, angles, or heights, remember the world of trigonometry is at your fingertips.