Trigonometry Formulas PDF for Class 11th

Trigonometry equations formulas for class 11th PDF

Trigonometry equations

Trigonometry Formulas PDF for Class 11th (Equations)

Trigonometry Formulas PDF for Class 11th : This sections illustrates the process of solving trigonometric equations of various forms. It also shows you how to check your answer three different ways: algebraically, graphically, and using the concept of equivalence.The following table is a partial lists of typical equations.

  1. TRIGONOMETRIC EQUATION:

An equation involving one or more trigonometrical ratios of unknown angles is called a trigonometrical equation

  1. SOLUTION OF TRIGONOMETRIC EQUATION:

A value of the unknown angle which satisfies the given equations is called a solution of the trigonometric equation.

(a)     Principal solution: the solution of the trigonometric equation lying in the interval [0, 2n].

(b)     General solution: since all the trigonometric functions are many one & periodic, hence there are infinite values of for which trigonometric functions have the same value. All such possible values of for which the given trigonometric function is satisfied is given by a general formula. such a general formula is called general solutions of the trigonometric equations.

trigonometry formulas pdf for class 11

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Trigonometry equations formulas for class 11th

  1. GENERAL SOLUTIONS OF SOME TRIGONOMETRIC EQUATIONS

(TO BE REMEMBERED):

  1. GENERAL SOLUTIONS OF SOME TRIGONOMETRIC EQUATIONS

(TO BE REMEMBERED):

(a)

(b)    

(c)

(d)

(e)

(f)      If

(g)

(h)     If

(i)      If

(j)      For

                  

 

(k)

(l)      If n is an odd integer then sin

(m)

 

GENERAL SOLUTION OF EQUATION

Consider,a

 

equation (I) has the solution only if

let

by introducing this auxiliary argumentequation (i) reduces to

Now this equation can be solved easily.

  1. GENERAL SOLUTION OF EQUATION OF FORM:

 

 

such an equation is solved by dividing equation by

  1. IMPORTANT TIPS:

(a)     For equations of the type sin  = k or cos  = k, one must check that .

(b)     Avoid squaring the equations, if possible, because it may lead to extraneous solutions.

(c)     Do not cancel the common variable factor form the two sides of the equations which are in a   product because we may loose some solutions.

(d)     The answer should not contain such values of , which make any of the terms undefined or infinite.

(e)     Check that denominator is not zero at any stage while solving equations.

(f)      (I)  If tanor secis involved in the equations should not be odd multiple of

(II) If cot or cosec is involved in the equation, should not be integral multiple of .

(g)     If two different trigonometric ratios such as tan and sec  are involved then after solving we cannot apply the usual formulae for general solution because periodicities of the function arenot same.

(h)     If L.H.S of the given trigonometric equation is always less than or equal to k and R.H.S is always greater than k, then no solution exists. If both the sides are equal to k for same value of,then solution exists and if they are equal for different value of , then solution does not exist.

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