1. The term "basic angle" typically refers to the smallest positive angle between the terminal side of a given angle and the x-axis in standard position. 2. It is often used in trigonometry to simplify the evaluation of trigonometric functions for angles beyond the first quadrant. 3. To find the basic angle $\theta_b$ for an angle $\theta$ measured in degrees: - If $\theta$ is in the first quadrant ($0^\circ \leq \theta \leq 90^\circ$), then $\theta_b = \theta$. - If $\theta$ is in the second quadrant ($90^\circ < \theta < 180^\circ$), then $\theta_b = 180^\circ - \theta$. - If $\theta$ is in the third quadrant ($180^\circ < \theta < 270^\circ$), then $\theta_b = \theta - 180^\circ$. - If $\theta$ is in the fourth quadrant ($270^\circ < \theta < 360^\circ$), then $\theta_b = 360^\circ - \theta$. 4. This concept helps in finding sine, cosine, and tangent values by relating them to their acute angle counterparts. 5. For example, if $\theta = 150^\circ$, then the basic angle is $\theta_b = 180^\circ - 150^\circ = 30^\circ$. 6. Understanding the basic angle simplifies trigonometric calculations and graph interpretations.