Matzic|

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.

1. 10.Sin²Θ + 4.SinΘ + 1 = 0
2. Cos²Θ – 4.SinΘ – 3 = 0
3. CosΘ + SinΘ = 1

In algebra, we can easier determine number of roots as per order of the equation but the situation is entirely different in trigonometry equation. In other words, algebraic equations have limited roots but trigonometry equations have unlimited roots. The order of the trigonometric equation does not play role in roots’ determination. That is the difference between trigonometric equations and algebraic quadratic equations.

I think, you understood Trigonometric equations have number of roots and set of these solutions called as Solution Set. Solution set is also called as General Solution.

Let see an example to have an idea before going to enter into concept.

SinΘ – 1/√2 = 0

It is an order one equation. In algebraic equation point of view, this equation should have one root or solution.

» SinΘ – 1/√2 = 0

» SinΘ = 1/√2

You can easily say the value of Θ is π/4 or 45º. We are wrong if we consider π/4 or 45º is only one solution. 3π/4, 5π/4, 7π/4 and etc satisfy by giving same value. So, all these values are also called as roots of this first order equation. So, we should not think that trigonometry functions have limited roots or solutions.

In this trigonometry equation, the first root π/4 is called as principle value. Similarly, the general value called as general value or solution which will be explained very clearly.