Trigonometric equations are those equations the unknown is the composition of the arguments of trigonometric functions.
Trigonometric equations are equations transcendent. That is, it causes a eparticularÄƒ solutions and then write the general solution is expressed in terms of a parameter and of the period of the trigonometric function.
Equations of this type are reduced to solving the equation and solve a trigonometric equation or two after one of the basic notations: sin x = t, cos x = t, tg x = t, ctg x = t.
5. Using the formula cos 2x = 1- 2 sin2 x we can obrain an first degree equation.
6. Because since , we can obtain the equation , i.e. an equation of type 3.
The Method 1.
Check if the equation has solutions of the form: .
It notes .
We have the formulas
And thus, we obtain the equation , with the condition .
The Method 2.
We write the substitutions , and we solve the equations system
The Method 3.
We make the substitution and we get
The equation has solutions if a2+b2>=c2.
Homogeneous equations are of the form:
We divide through cosnx and we get:
And if we note tgx = y then we get:
We have 3 ways of solving:
Method 1. I note and I use the formulas , .
Method 2. I note and I get the equation which it resolves with condition .
Method 3. I note and the equation becomes
We rise the identity at the powers n, n-1, …., 3,2
Then we note sin 2x = t and we get an equation rank n with the unknown t.
Th The equations having the form as
We use the formulas
3. Equations containing products form:
Convert products in the amounts or differences sinus (sine) or cosines (cosine).
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