Trigonometric equation is an equation that contains any of the trigonometric functions - sine, cosine, tangent, cosecent, secent and cotangent. By the solution of trigonometric equation, we mean to determine the value of the unknown angle which satisfies given trigonometric equation. The examples of trigonometric equations are:

- $\sin \theta$ = $\frac{\sqrt{3}}{2}$
- $\cos ^{2}\theta -3\cos \theta +2=0$

Trigonometric functions are periodic, so there is no single solution for a trigonometric equation. There are general forms of solutions of trigonometric functions sin, cos and tan. These general solutions are given below:

**General Solution for Sine**

Where, n is an integer.

**General Solution for Cosine**

Where, n is an integer.

**General Solution of Tangent**

Where, n is an integer.

**Let us take an example:**

**Example:** Solve $2\sin \theta =1$

**Solution:** $2\sin \theta =1$

$\sin \theta = $\frac{1}{2}$

$\sin \theta =\sin $$\frac{\pi }{6}$

$\theta =n\pi +(-1)^{n}$$\frac{\pi }{6}$

Where, n = 0, 1, 2, 3, .......

at n = 0,

$\theta =$$\frac{\pi }{6}$

at n = 1,

$\theta =$$\frac{5\pi }{6}$

at n = 2,

$\theta =$$\frac{13\pi }{6}$

at n = 3,

$\theta =$$\frac{17\pi }{6}$

Hence, $\theta =$$\frac{\pi }{6}$, $\frac{5\pi }{6}$, $\frac{13\pi }{6}$, $\frac{17\pi }{6}$, .......

Related Calculators | |

Equation Solving Calculator | Solve a System of Equations Calculator |

solve cubic equation calculator | Solve Differential Equation Calculator |