Question

Give all the trigonometric identities.

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Trigonometric Identities are equations that are true for Right Angled Triangles. (If it is not a Right Angled Triangle go to the Triangle Identities page.)

Each side of a right triangle has a name:





Adjacent is always next to the angle

And Opposite is opposite the angle

We are soon going to be playing with all sorts of functions, but remember it all comes back to that simple triangle with:

Angle θ

Hypotenuse

Adjacent

Opposite

Sine, Cosine and Tangent

The three main functions in trigonometry are Sine, Cosine and Tangent.

They are just the length of one side divided by another

For a right triangle with an angle θ :



Sine Function:

sin(θ) = Opposite / Hypotenuse

Cosine Function:

cos(θ) = Adjacent / Hypotenuse

Tangent Function:

tan(θ) = Opposite / Adjacent

For a given angle θ each ratio stays the same 

no matter how big or small the triangle is

 

When we divide Sine by Cosine we get:

sin(θ)cos(θ) = Opposite/HypotenuseAdjacent/Hypotenuse = OppositeAdjacent = tan(θ)

So we can say:

tan(θ) = sin(θ)cos(θ)

That is our first Trigonometric Identity.