PowerPoint Presentation

[Audio] Hello everyone I Aryan Wadhwa student of tenth blue of jesus saviour's school and now going to present my ppt on TRIGONOMETERY.

[Audio] What Is Trigonometery ?? * Trigonometry : the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine ( sin), cosine ( cos), tangent (tan), cotangent ( cot), secant ( sec), and cosecant ( cosec). * Trigonometry developed from a need to compute angles and distances in such fields as astronomy, mapmaking, surveying, and artillery range finding. Problems involving angles and distances in one plane are covered in plane trigonometry..

* The word trigonometry comes from the Greek words trigonon (“triangle”) and metron (“to measure”). Trigonometry in the modern sense began with the Greeks . Hipparchus ( c. 190–120 BCE ) was the first to construct a table of values for a trigonometric function . * The first major ancient work on trigonometry to reach Europe intact after the Dark Ages was the Almagest by Ptolemy ( c. 100–170 CE )..

Trigonometric Ratios. 01. Trigonometric IDENTITIES.

Trigonometric Ratios. Trigonometric Ratios Sin θ Opposite Side to θ/ Hypotenuse Cos θ Adjacent Side to θ/ Hypotenuse Tan θ Opposite Side/Adjacent Side & Sin θ/Cos θ Cot θ Adjacent Side/Opposite Side & 1/tan θ Sec θ Hypotenuse/Adjacent Side & 1/ cos θ Cosec θ Hypotenuse/Opposite Side & 1/sin θ.

Trigonometric Ratios Angles (In Degrees) 0° 30° 45° 60° 90° sin 0 1/2 1/√2 √3/2 1 cos 1 √3/2 1/√2 1/2 0 tan 0 1/√3 1 √3 ∞ cot ∞ √3 1 1/√3 0 cosec ∞ 2 √2 2/√3 1 sec 1 2/√3 √2 2 ∞.

TRIGONOMETRIC. IDENTITIES. * Cos 2 θ + Sin 2 θ = 1 * Sec 2 θ - Tan 2 θ = 1 * Cosec 2 0 - Cot 2 0 = 1.

[Audio] APPLICATIONS OF Trigonometery IN DAILY LIFE Trigonometry to Measure Height of a Building or a Mountain. Trigonometry in Aviation Trigonometry in Criminology Trigonometry in Marine Biology. Trigonometry in Navigation.

[Audio] Let's consider an example . One day a boy named Rahull went to hill station where he saw a beautiful tree . It was 10 metre far from him. He saw a top of tree . It formed angle of elevation of 45 degree . He wanted to Find the height of tree . Now by easily using concept of Trigonometery he found the height of tree which was 10 m long ..

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[Audio] Trigonometry IS ALSO use to measure height of a building or a mountain. For example : Height of Boy is 5 feet . Height of Building is AC plus 5 feet . Distance between Building & Boy is 20 feet . Angle Of Elevation is 30 degree . Tan theta is AC by BC . Tan 30 degree is AC by 20 . AC is equal to 11.548 feet ..

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[Audio] Aviation technology has evolved with many upgrades in the last few years. It has taken into account the speed, direction and distance as well as the speed and direction of the wind. The wind plays a vital role in when and how a flight will travel. This equation can be solved by using trigonometry..

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[Audio] Trigonometry is even used in the investigation of a crime scene. The functions of trigonometry are helpful to calculate a trajectory of a projectile and estimate the causes of a collision in a car accident. Further, it is used to identify how an object falls or at what angle the gun is shot..

[Audio] THANK YOU. THANK YOU.