It is human to err.
But to err repeatedly is wrong.
Knowing the scope of a mathematical tools or concepts is a necessary part to handling math well.
In trigonometry, you need to understand the principles of using these trigonometrical functions.
What is the confine of their usage?
What is the factors before proper usage?
Cited below is a common mistake in using trigonometric operation improperly.
It is the solution of parameter for specific triangle.
Determine the length of "a" given angle A, angle B and length "b".
Incorrect working to calculate length "a":-
sin A = a / b ==> a = (b) times (sin A). ===> Incorrect!
To understand sine operation, you need to know its condition of usage.
Trigonometric function sine, cosine and tangent is defined using "right-angled" triangle.
To solve for the above problem, you need to know that angle B is not right-angled.
Therefore, you cannot simply use sin A = a/b.
Angle B has to be of "right-angle" or 900 for that to be correct.
The proper method is to apply the "Law of Sine" for this particular example.
"Law of Sine" : (a / sin A) = (b / sin B) = (c / sin C)
Applying this Sine Law does not require the angles to be at right-angle.
However, do note that you need to know more parameters in the triangle to use the "Law of Sine". Example is the Angle B.
Message: You need to understand the scope of trigonometric operations to apply them correctly.
Application of math principles and concepts requires mental preparation of selecting and strategising correct technique.
And this is what make maths learning interesting.