
4. Na grafu funkcije $f(x)=\sin x$ sta točki $A\left(\frac{\pi}{3}, f\left(\frac{\pi}{3}\right)\right)$ in $B\left(\frac{\pi}{6}, f\left(\frac{\pi}{6}\right)\right)$. Zapiši enačbo premice, ki poteka skozi točki $A$ in $B$. Koeficienti naj bodo določeni natančno (brez uporabe žepnega računala).

4. Najprej izračunamo ordinati danih točk: $f\left(\frac{\pi}{3}\right)=\sin \frac{\pi}{3}=\frac{\sqrt{3}}{2}$ in $f\left(\frac{\pi}{6}\right)=\sin \frac{\pi}{6}=\frac{1}{2}$. Nato izračunamo smerni koeficient $k=\frac{\frac{1}{2}-\frac{\sqrt{3}}{2}}{\frac{\pi}{6}-\frac{\pi}{3}}$. Zapis poenostavimo $k=\frac{3(\sqrt{3}-1)}{\pi}$. Nato v enačbo premice vstavimo ustrezne podatke $y=k\left(x-x_{1}\right)+y_{1}=\frac{3(\sqrt{3}-1)}{\pi}\left(x-\frac{\pi}{3}\right)+\frac{\sqrt{3}}{2}$. Zapis poenostavimo in dobimo $y=\frac{3(\sqrt{3}-1)}{\pi} x+1-\frac{\sqrt{3}}{2}$.

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-13.jpg?height=69&width=1636&top_left_y=2470&top_left_x=210)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-13.jpg?height=69&width=1639&top_left_y=2527&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-13.jpg?height=94&width=1642&top_left_y=2580&top_left_x=207)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-14.jpg?height=77&width=1642&top_left_y=216&top_left_x=204)

Vstavljeni podatki v enačbo premice ................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-14.jpg?height=85&width=1642&top_left_y=320&top_left_x=207)
