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Trigonometry ... Is All About Triangles

Solving triangles using sin,cos and tan angles

Date : 30/04/2015

Author Information

Sandhya

Uploaded by : Sandhya
Uploaded on : 30/04/2015
Subject : Maths

The triangle of most interest is the right-angled triangle. The three sides of a right angled triangle are, Adjacent,Hypotenuse and opposite. Adjacent is adjacent (next to) to the angle ? Opposite is opposite the angle ? the longest side is the Hypotenuse.

"Sine, Cosine and Tangent"

Trigonometry is good at find a missing side or angle in a triangle.

The special functions Sine, Cosine and Tangenthelp us!

They are simply one side of a triangle divided by another.

For any angle "?": Sine Function: sin(?) = Opposite / Hypotenuse Cosine Function: cos(?) = Adjacent / Hypotenuse Tangent Function: tan(?) = Opposite / Adjacent (Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.)

Example: What is the missing length here?

We know the Hypotenuse We want to know the Opposite Sine is the ratio of Opposite / Hypotenuse

calculator-sin-cos-tan Get a calculator, type in "45", then the "sin" key:

sin(45°) = 0.7071...

Now multiply by 20 (the Hypotenuse length):

Opposite length = 20 × 0.7071... = 14.14 (to 2 decimals)

A big part of Trigonometry is Solving Triangles. "Solving" means finding missing sides and angles.

For eg:

Total angles of a right angled triangle is 180 degree Angle A=76 degree, B= 34 degree. Find angle C.

So C=180-76-34=70.

It is also possible to find missing side lengths and more. The general rule is:

When we know any 3 of the sides or angles we can find the other 3 (except for the three angles case)

Other Functions (Cotangent, Secant, Cosecant)

Similar to Sine, Cosine and Tangent, there are three other trigonometric functions which are made by dividing one side by another:

Cosecant Function: csc(?) = Hypotenuse / Opposite Secant Function: sec(?) = Hypotenuse / Adjacent Cotangent Function: cot(?) = Adjacent / Opposite

To Sum up the concept of Trignometry:

The Trigonometric Identities are equations that are true for all right-angled triangles.

triangle The Triangle Identities are equations that are true for all triangles (they don`t have to have a right angle).

This resource was uploaded by: Sandhya