Trigonometric Functions

The period of a trigonometric function is the length of one complete cycle of the function. For sine and cosine functions, the period is typically $$2\theta$$ , while for tangent and cotangent, it is $$\theta$$ .

The period of the function $$y = \tan(2x)$$ is $$\frac{\theta}{2}$$ , which is $$\frac{\theta}{2} = \frac{\theta}{2} = \frac{\theta}{2}$$ .

Domain: D: $$(-\frac{\theta}{2}, \frac{\theta}{2})$$ , Range: R: $$(-\frac{\theta}{2}, \frac{\theta}{2})$$ .

The amplitude of the function $$y = 3\text{sin}(x)$$ is 3.

The amplitude of the function $$y = -2\text{cos}(x)$$ is 2 (amplitude is always positive).

The domain of the function $$y = \text{sin}(x)$$ is D: $$(-\theta, \theta)$$ .

The range of the function $$y = \text{sin}(x)$$ is R: $$[-1, 1]$$ .

The amplitude of the function $$y = 5\text{sin}(3x) - 1$$ is 5.

The period of the function $$y = \text{cos}(4x)$$ is $$\frac{2\theta}{4} = \frac{\theta}{2}$$ .

The amplitude of the function $$y = 2\text{sin}(x) + 1$$ is 2.