We have learned general solution of sine previously. Now, we are going to learn the concept of general solution of Cosine. The general solution of Cosine trigonometry function is helpful to solution trigonometric equations which consist Cosine terms. Let take CosΘ = C is a trigonometric function where C is the constant value which varies from 0 to 1.
CosΘ = C
Let us assume, the corresponding value is Cosα for every constant value for our convenience.
CosΘ = Cosα
CosΘ – Cosα = 0
We have already proved that CosC – CosD = – 2.Sin[(C + D)/2].Sin[(C – D)2]
We have learned the way to find roots of a quadrant equation. Now, we are going to learn the mathematical method to
SinΘ = C
Where C is a constant value which may be anything between 0 to 1. Let us assume the corresponding value of the constant value would be Sinα. So, we can write above trigonometric equation as
SinΘ = Sinα
Now we can write this as an equation
SinΘ – Sinα = 0
As we already know that
We have learned lots of concepts of trigonometry, derived several mathematical trigonometry fundamentals and solved different types of trigonometry problems previously. Now, it is time to learn one more important concept regarding trigonometry. This mathematical concept is called as Trigonometric equations.
In Algebra, quadratic equation ax2 + bx + c = 0 or similar equations often come into picture. Mathematically we know that this kind of quadratic equation has two roots. Similarly, we have already developed a formula to find general solution of roots.
Just like algebraic quadratic equation, we are going to deal equations with trigonometry functions. You can also see sample trigonometric equations below for better understanding purpose.
