Question

A unit circle is shown in the coordinate plane. An angle of 5pi/3 radians is also drawn on the unit circle. Using g the diagram, determine the value of Csc 5pi/3

Answer 1

Answer: csc 5pi/3 = -(2root3)/3

Step-by-step explanation:

Csc 5pi/3 is 1/sin(5pi/3). Sin will always be the y value of the point and cosine is the x value. So 1/(-root3/2) = -2/root3. We can't have the denominator containing a root so we multiply both the denominator and numerator by root3 to get the answer -(2root3)/3.

Answer 2

Step-by-step explanation:

From this diagram we can get the sine and cosine of the given angle, because they are the coordinates of the point:

The cosecant is the reciprocal of the sine:

`\csc \theta=(1)/(\sin \theta)`

Therefore:

`\begin{gathered} \text{if }\cdot\sin ((5\pi)/(3))=-\frac{\sqrt[]{3}}{2} \\ \text{ then we have:} \\ \csc ((5\pi)/(3))=(1)/(\sin ((5\pi)/(3)))=\frac{1}{-\frac{\sqrt[]{3}}{2}}=-\frac{2}{\sqrt[]{3}}=-\frac{2\sqrt[]{3}}{3} \end{gathered}`

Answer:

csc (5pi/3) = -2√3/3