Subjects trigonometry

Tangent Negative Angle 7A4741

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1. The problem asks to find $\tan(-0)$ given $\cos 0 = 0.8$ and $\sin 0 = 0.6$. 2. Recall the definition of tangent: $$\tan \theta = \frac{\sin \theta}{\cos \theta}$$ 3. Also, use the identity for tangent of a negative angle: $$\tan(-\theta) = -\tan \theta$$ 4. First, calculate $\tan 0$: $$\tan 0 = \frac{\sin 0}{\cos 0} = \frac{0.6}{0.8}$$ 5. Simplify the fraction: $$\frac{0.6}{0.8} = \frac{\cancel{0.6}}{\cancel{0.8}} = \frac{3}{4} = 0.75$$ 6. Now apply the negative angle identity: $$\tan(-0) = -\tan 0 = -0.75$$ 7. Therefore, the final answer is: $$\boxed{-0.75}$$