# How do you find the important points to graph y = (1/2)sin(x - pi)?

You can use the given trigonometric equation to compute for the rectangular coordinate points $\left(x , y\right)$, then use these points to draw your graph.

#### Explanation:

From the given equation
$y = \frac{1}{2} \cdot \sin \left(x - \pi\right)$

Compute the rectangular coordinate points $\left(x , y\right)$

$x$ in degrees and radians

$\text{degrees x y " " " " y in decimals}$
$\text{ } 0$$\text{ } 0$$\text{ } 0$$\text{ } 0$

$\text{ } 30$$\text{ } \frac{\pi}{6}$$\text{ } - \frac{1}{4}$$\text{ } - 0.25$

$\text{ } 45$$\text{ } \frac{\pi}{4}$$\text{ } \frac{- \sqrt{2}}{4}$$\text{ } - 0.3535533906$

$\text{ } 60$$\text{ } \frac{\pi}{3}$$\text{ } \frac{- \sqrt{3}}{4}$$\text{ } - 0.4330127019$

$\text{ } 90$$\text{ } \frac{\pi}{2}$$\text{ } - \frac{1}{2}$$\text{ } - 0.5$

$\text{ } 120$$\text{ } \frac{2 \pi}{3}$$\text{ } \frac{- \sqrt{3}}{4}$$\text{ } - 0.4330127019$

$\text{ } 135$$\text{ } \frac{3 \pi}{4}$$\text{ } \frac{- \sqrt{2}}{4}$$\text{ } - 0.3535533906$

$\text{ } 150$$\text{ } \frac{5 \pi}{6}$$\text{ } - \frac{1}{4}$$\text{ } - 0.25$

$\text{ } 180$$\text{ } \pi$$\text{ } 0$$\text{ } 0$

$\text{ } 210$$\text{ } \frac{7 \pi}{6}$$\text{ } \frac{1}{4}$$\text{ } 0.25$

$\text{ } 225$$\text{ } \frac{5 \pi}{4}$$\text{ } \frac{\sqrt{2}}{4}$$\text{ } 0.3535533906$

$\text{ } 240$$\text{ } \frac{4 \pi}{3}$$\text{ } \frac{\sqrt{3}}{4}$$\text{ } 0.4330127019$

$\text{ } 270$$\text{ } \frac{3 \pi}{2}$$\text{ } \frac{1}{2}$$\text{ } 0.5$

$\text{ } 300$$\text{ } \frac{5 \pi}{3}$$\text{ } \frac{\sqrt{3}}{4}$$\text{ } 0.4330127019$

$\text{ } 315$$\text{ } \frac{7 \pi}{4}$$\text{ } \frac{\sqrt{2}}{4}$$\text{ } 0.3535533906$

$\text{ } 330$$\text{ } \frac{11 \pi}{6}$$\text{ } \frac{1}{4}$$\text{ } 0.25$

$\text{ } 360$$\text{ } 2 \pi$$\text{ } 0$$\text{ } 0$