Solving Trigonometric Equations

In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

The cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

The Pythagorean identity states that for any angle x, $$\tan^2 x + 1 = \frac{1}{\text{cos}^2 x}$$ .

The general solution is $$x = \tan^{-1}(k) + n\frac{\text{pi}}{2}$$ , where n is any integer.

The solutions are $$x = n\text{pi}$$ , where n is any integer.

The range of the sine function is from -1 to 1, inclusive.

The range of the cosine function is also from -1 to 1, inclusive.

The solutions are $$x = \frac{\text{pi}}{6} + 2n\text{pi}$$ and $$x = \frac{5\text{pi}}{6} + 2n\text{pi}$$ , where n is any integer.

To convert degrees to radians, multiply by $$\frac{\text{pi}}{180}$$ . To convert radians to degrees, multiply by $$\frac{180}{\text{pi}}$$ .

A trigonometric equation is an equation that involves trigonometric functions of a variable.