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MATHMAA

math-formula-sheet-generalSolutions

General Solutions  is a topic in Trigonometry, the formula related to General Solutions are provided in this math-formula-sheet-generalSolutions. These formula will help the students who are in 10th, 11th, 12th and College Grade too.

In this we get Principal Value and General solution of the angle.

PRINCIPAL SOLUTIONS:

The solutions of a trigonometric equations for which 0$$\leq x< 2\prod$$ are called Principal solutions.

GENERAL SOLUTIONS:

The expressions involving integer 'n' which gives all solutions of a Trigonometric equation is called the "general solution".

Principal Value and General solution of Sin, Cos, Tan as follows:

1) If Sin(x)= 0

Principal value of x = 0 as Sin(x)=Sin(0)

General solution of x = n$$\prod$$, n$$\epsilon Z$$, Z is set of integers.

2)If Cos(x)=0 then

Principal value of x =$$\frac{\prod}{2}$$

General Solution of x = (2n+1)$$\frac{\prod}{2}$$.

3)If Sin(x)=Sin(y) then

Principal value of x = y and

General Solution of x = $$n\prod+(-1)^{n}y$$, where n$$\epsilon Z$$

4) If Cos(x)= Cos(y) then

Principal value of x = y and

General Solution of x =$$2n\prod\pm y$$, where n$$\epsilon Z$$.

5)If Tan(x)= Tan(y) then

Principal value of x=y and

General solution of x =$$n\prod+y$$., where $$n\epsilon Z$$.

6) If $$Sin^{2}(x)=Sin^{2}(y)$$, or $$Cos^{2}(x)=Cos^{2}(y)$$ , or $$Tan^{2}(x)=Tan^{2}(y)$$then

Principal value of x=y and

General solution of x= $$n\prod \pm y$$. , $$n\epsilon Z$$.