Oblicz

[avleyi]

Kąt \( \alpha \) jest ostry i \(\cos \alpha = \frac{ \sqrt{7} }{4} \). Oblicz \(2+\sin^3 \alpha +\sin \alpha \cdot \cos^2 \alpha \)

[Jerry]

\((\alpha\in(0^\circ;90^\circ)\wedge\cos \alpha = \frac{ \sqrt{7} }{4})\So\sin\alpha=\sqrt{1-{7\over16}}={3\over4}\)

\(w(\alpha)=2+\sin^3 \alpha +\sin \alpha \cdot \cos^2 \alpha=2+\sin\alpha\cdot(\sin^2 \alpha +\cos^2 \alpha)=2+{3\over4}\cdot1=2,75\)

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