## Monday, 4 August 2008

### Interpretation of Trigonometric Functions

What are the trigonometric operators or functions in mathematics?

They are the three basic operators, namely:

• Sine (written as "sin")

• Cosine (written as "cos")

• Tangent (written as "tan")

They represent ratio or number. They are related to angle and sides of a triangle.

How are they expressed mathematically?

Example:
cos Y = 0.707 with "Y" representing the angle in question.

In words, the meaning of the above example is "The cosine of angle Y is the number 0.707".

The word "cos" is performing a trigonometrical operation on the angle Y.
(This goes for the other trigonometic functions).

Moving forward with that understanding, it is clear that the "cos" has the same operational rank as the basic mathematical operators +, -, x, and /.

"cos" is not a variable!

"cos" cannot stand alone.

Cos A = 0.707 does not mean "cos" multiply "A" = 0.707.

What it really meant is angle A is trigonometrically operated using "cos" to reflect a number.

"Cos" and "A" has to be together to form a useful meaning on the maths function.

But note, "cos" can be rewritten as cos-1 to represent another trigonometric function of Inverse Cosine.

Example: cos A = 0.707 ===> A = cos-1 0.707

It means , in words, the inverse cosine of 0.707 is the angle A.

Here the operator "cos" can be taken separately and moved over to the opposite side of the equal sign to the number ratio 0.707 in order to get the numerical value of the angle A.

Here the emphasis should be taken that "cos-1", though works like a variable (in this case), is done to fulfill the function of "Inverse cosine" and not as a variable.

Common trigonometry mistake by students / maths learners is to treat the "cos" (or the others) as a variable to be operated upon.

Message:
"cos" is not a number and therefore cannot be a variable. It has to work hand-in-hand with an angle to be meaningful. Make sense?

I repeat, "cos" is a function to operate with an angle. It cannot stand alone. Clear ?
Good!

:)
.