what do you mean by trigonometric identities ?
Share
what do you mean by trigonometric identities ?
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
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.
Cosecant, Secant and Cotangent
We can also divide "the other way around" (such as Adjacent/Opposite instead of Opposite/Adjacent):
Cosecant Function:
coc(θ) = Hypotenuse / Opposite
Secant Function:
sec(θ) = Hypotenuse / Adjacent
Cotangent Function:
cot(θ) = Adjacent / Opposite
Hope this helps :)