Lesson 17 Solving Trigonometric Equations

A trigonometric equation is an equation that involves trigonometric functions of a variable, typically an angle, such as sine, cosine, or tangent.

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

To solve, find the angle(s) where $$\text{sin}(\theta) = \frac{1}{2}$$ , which are $$\theta = \frac{\text{\text{pi}}}{6} + 2n\text{\text{pi}}$$ and $$\theta = \frac{5\text{\text{pi}}}{6} + 2n\text{\text{pi}}$$ .

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

The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane, used to define trigonometric functions.

$$\text{sin}(0) = 0$$ and $$\text{cos}(0) = 1$$ .

The Pythagorean identity states that $$\text{sin}^2(\theta) + \text{cos}^2(\theta) = 1$$ for any angle $$\theta$$ .

The solutions are $$\theta = \frac{\text{pi}}{2}$$ and $$\theta = \frac{3\text{pi}}{2}$$ .

The period of the sine function is $$2\text{pi}$$ .

Sine and cosine are both periodic functions, but sine represents the y-coordinate of a point on the unit circle, while cosine represents the x-coordinate.