Subjects trigonometry

Sin Pi Theta

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Sin Pi Theta


1. **Problem Statement:** Find the value of $\sin(\pi - \theta)$ in terms of $\sin \theta$ or $\cos \theta$. 2. **Formula and Explanation:** Use the sine subtraction formula or the unit circle properties. The sine of an angle $\pi - \theta$ is related to the sine of $\theta$ by the identity: $$\sin(\pi - \theta) = \sin \pi \cos \theta - \cos \pi \sin \theta$$ Recall that $\sin \pi = 0$ and $\cos \pi = -1$. 3. **Intermediate Work:** Substitute these values: $$\sin(\pi - \theta) = 0 \cdot \cos \theta - (-1) \cdot \sin \theta = \sin \theta$$ 4. **Conclusion:** Therefore, $\sin(\pi - \theta) = \sin \theta$. 5. **Answer:** The correct choice is d. $\sin \theta$.