Answer:
[tex]A\colon\csc \text{ }\frac{4\pi}{3}\text{ = -}\frac{2\sqrt[]{3}}{3}[/tex]
Explanation:
Here, we want to get the cosec value of the given term
Mathematically, we know that:
[tex]co\sec \text{ }\alpha\text{ = }\frac{1}{\sin \text{ }\alpha}[/tex]
Now, we need to know the quadrant in which the angle belong
Mathematically, we know that pi in radians is equal to 180 degrees
Thus,we have it that:
[tex]\frac{4\pi}{3}\text{ = }\frac{4\times180}{3}\text{ = 240}\degree[/tex]
As we know, the angle belongs to the third quadrant
On the third quadrant, the value of sine is negative
Thus, the cosec value is expected to be negative too
The terminal angle of 240 is 60
Thus,we have it that:
[tex]\sin (240\degree)\text{ = -sin(60}\degree)\text{ = -}\frac{\sqrt[]{3}}{2}[/tex]
Now, we have to find the reciprocal of this
We have this as:
[tex]\csc \text{ }\frac{4\pi}{3}\text{ = -}\frac{2}{\sqrt[]{3}}\text{ = -}\frac{2\sqrt[]{3}}{3}[/tex]
