What is Trigonometric Function?
It is a function of an angle or an abstract quantity that is used in trigonometry wherein the six trigonometric functions are also part of it.
In mathematics, equations can be classified as an identity or a conditional equation.
Are you excited to know their meaning and difference? Let's begin!
Identity Equation is an equation whose two sides are identical. This equation is also true for all real numbers.
EXAMPLE
IT'S JUST EASY TO UNDERSTAND RIGHT? NOW LET'S STUDY THE OTHER EQUATION WHICH IS CONDITIONAL EQUATION.
CONDITIONAL EQUATION is an equation that is only satisfied by a specific real number.
EXAMPLE
THE BOTTOMLINE FOR THIS TWO EQUATION IS THAT BEFORE SOLVING THE GIVEN,
WE MUST FIRST PROCESS AND STUDY THE PROBLEM BEFORE ANSWERING THEM BECAUSE SOMETIME IT'S ALREADY CLEAR WHETHER IT'S AN IDENTITY OR A CONDITIONAL EQUATION SO FOR US TO DEAL WITH IT EASIER.
BEFORE I'LL SHOW YOU THE NEXT LESSON, WE MUST REMEMBER THESE THINGS!
- always check if there still numbers that we can factor.
- get their common denominator
- rewrite everything in SINE and COSINE.
MAGIC HEXAGON - this is the tool that will provide our needs in mathematics.
- this will help a lot in answering the different identities in trigonometric functions.
RECIPROCAL IDENTITIES
In the reciprocal identities, just look at the opposite vertices of the hexagon. Check at the Sin 𝜽, it has the Csc 𝜽 in the opposite same through with the other functions.
Remember: if the function starts with letter s, its reciprocal is c. If the function starts with letter c, its reciprocal is s. And tan will always have the reciprocal of cot.
QUOTIENT IDENTITIES
In finding quotient identities, just look at the arrangement in the hexagon. Tan 𝜽 will go to Sin 𝜽 then Cos 𝜽! Same goes with the Cot 𝜽. Cot 𝜽 will go to Cos 𝜽 then Sin 𝜽.
To help you remember: memorized these tips!
TSC (tangent - sine - cosine)
CSC (cotangent - cosine - sine)
PYTHAGOREAN IDENTITIES
To find the Pythagorean identities, square each function in the hexagon and follow the arrows in it.
REMEMBER!
Sine² θ + Cos² θ = 1
1 + Cot² θ = Csc² θ
Tan² θ +1= Sec² θ
It doesn't matter if you'll use the table or the magic hexagon for as long as you're using the way on where you are more comfortable with!
Cheers to more videos for everyone!!