Question

GIVEN ANGLE: theta = 2pi/31. Draw the given angle in standard position2. Find the label and the reference angle3. Determine the exact values for the Sides of the triangle formed with the reference point and the x-axis with the value of the hypotenuse as 1. label the sides of on the picture of the triangle.4. write out the EXACT Answer to the 6 trig functions: sin theta= cos theta= tan theta= csc theta= sec theta= cot theta=

Answer 1

Reference Angle is the angle formed by the terminal ray of the original angle and the x-axis.

so, from the diagram we can calaculte it to be...

`\begin{gathered} \text{The value conversion of : }(2\pi)/(3)\text{ = }\frac{2\text{ }*180}{3}\text{ = }(360)/(3)=120^o \\ \end{gathered}`

Then the Reference Angle = 180 -120 = 60

`\begin{gathered} u\text{sing sin 60 = }(k)/(1) \\ k\text{ = sin 60 }*1 \\ k\text{ = 0.8666} \\ \text{where k represent the side of the formed Triangle.} \\ \end{gathered}`

sin 60 = 0.86660

cos 60 = 0.5

tan 60 = 1.732