Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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**Unit Circle and Trigonometric Table** **Diagram Explanation:** The diagram above represents the unit circle, which is a circle with a radius of 1 centered at the origin of a coordinate system. The circle is divided into twelve equal segments by orange lines, indicating standard angles used in trigonometry. The x-axis and y-axis intersect at the center of the circle. - The angle \( t = \frac{\pi}{6} \) is shown explicitly with an orange line extending from the origin forming one of the segments. - The red points on the circle highlight key positions corresponding to angles measured in radians, commonly used in trigonometric calculations. **Trigonometric Table:** The table provided below the diagram lists angles \( t \) in radians alongside spaces for the corresponding sine \(\sin(t)\) and cosine \(\cos(t)\) values: \[ \begin{array}{|c|c|c|} \hline t & \sin(t) & \cos(t) \\ \hline 0 & & \\ \hline \frac{\pi}{6} & & \\ \hline \frac{\pi}{3} & & \\ \hline \frac{\pi}{2} & & \\ \hline \frac{2\pi}{3} & & \\ \hline \frac{5\pi}{6} & & \\ \hline \pi & & \\ \hline \frac{7\pi}{6} & & \\ \hline \frac{4\pi}{3} & & \\ \hline \frac{3\pi}{2} & & \\ \hline \frac{5\pi}{3} & & \\ \hline \frac{11\pi}{6} & & \\ \hline \end{array} \] Each row corresponds to a specific angle \( t \) where students or users should determine and fill in the sine and cosine values based on their understanding of the unit circle.
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Transcribed Image Text:**Unit Circle and Trigonometric Table** **Diagram Explanation:** The diagram above represents the unit circle, which is a circle with a radius of 1 centered at the origin of a coordinate system. The circle is divided into twelve equal segments by orange lines, indicating standard angles used in trigonometry. The x-axis and y-axis intersect at the center of the circle. - The angle \( t = \frac{\pi}{6} \) is shown explicitly with an orange line extending from the origin forming one of the segments. - The red points on the circle highlight key positions corresponding to angles measured in radians, commonly used in trigonometric calculations. **Trigonometric Table:** The table provided below the diagram lists angles \( t \) in radians alongside spaces for the corresponding sine \(\sin(t)\) and cosine \(\cos(t)\) values: \[ \begin{array}{|c|c|c|} \hline t & \sin(t) & \cos(t) \\ \hline 0 & & \\ \hline \frac{\pi}{6} & & \\ \hline \frac{\pi}{3} & & \\ \hline \frac{\pi}{2} & & \\ \hline \frac{2\pi}{3} & & \\ \hline \frac{5\pi}{6} & & \\ \hline \pi & & \\ \hline \frac{7\pi}{6} & & \\ \hline \frac{4\pi}{3} & & \\ \hline \frac{3\pi}{2} & & \\ \hline \frac{5\pi}{3} & & \\ \hline \frac{11\pi}{6} & & \\ \hline \end{array} \] Each row corresponds to a specific angle \( t \) where students or users should determine and fill in the sine and cosine values based on their understanding of the unit circle.
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