Answer:
[tex]\frac{7}{6} \pi\ radians[/tex]
Step-by-step explanation:
Conversion between Degree and Radian:
Bear in mind that 1 whole circle has 360°, which is same as 2π radians. Therefore:
Converting x° to radian:
degree : radian = degree : radian
360° : 2π rad = x° : radian
180° : π rad = x° : radian
[tex]\boxed{radian=\frac{x^o}{180^o}\times\pi\ rad }[/tex]
Converting x rad to degree:
degree : radian = degree : radian
360° : 2π rad = degree : x rad
180° : π rad = degree : x rad
[tex]\boxed{degree=\frac{x\ rad}{\pi\ rad}\times180^o}[/tex]
Given:
Interval = [π, 3π/2]
[tex]\displaystyle=\left[\left(\frac{\pi}{\pi} \times180^o\right),\left(\frac{3\pi}{2\pi} \times180^o\right)\right][/tex]
[tex]=[180^o,270^o][/tex] → within Quadrant 3 where y-value is negative
→ sin value is also negative
[tex]\displaystyle sin\ s=-\frac{1}{2}[/tex]
[tex]\displaystyle\frac{y}{r} =\frac{-1}{2}[/tex]
The angle that meet the y : r ratio is 30° beyond the negative x-axis (see the picture).
The total angle start from positive x-axis = 180° + 30° = 210°
Convert into radian:
[tex]radian=\frac{210^o}{180^o}\times\pi\ rad[/tex]
[tex]=\frac{7}{6} \pi\ radians[/tex]
