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Suppose π/2 < a < π. Using the trigonometric identities and the fact that sin(α) = 4/5. Find cos(α). Show all working |
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Answer» \(\frac{\pi}{2}<\alpha<\pi\) sin \(\alpha=\frac{4}{5}\) \(\alpha\) lies in second quadrant so , cos \(\alpha\) is negative ∵ sin2 \(\alpha\) + cos2 \(\alpha\) = 1 ⇒ cos \(\alpha\) = \(\pm\sqrt{1-sin^2\alpha}\) But cos \(\alpha\) is negative ∴ Cos \(\alpha\) = \(-\sqrt{1-sin^2\alpha}\) \(=-\sqrt{1-(\frac{4}{5})^2}\) \(=-\sqrt{1-(\frac{4}{5})^2}\) \(=-\sqrt{\frac{25-16}{25}}{}\) \(=-\sqrt{\frac{9}{25}}=-\frac{3}{5}\) |
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