Question 1207211
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If you are allowed access to the Unit Circle then it's best to use it
<img src = "https://www.mathsisfun.com/geometry/images/circle-unit-radians.svg">
Image Source:
https://www.mathsisfun.com/geometry/unit-circle.html


The x and y coordinates of the terminal point represent the cosine and sine values respectively.


For example, 
cos(pi/3) = 1/2
sin(pi/3) = sqrt(3)/2
pi/3 radians = 60 degrees


Focus on the upper right corner known as quadrant I.
Notice 30-60-90 triangles are useful for the 30 and 60 degree angles.
A 45-45-90 triangle is useful for the 45 degree angle. 
Use the appropriate template for each.


Once you've memorized the items in the 1st quadrant, you can then use symmetry to apply things to the other quadrants.


One last thing to note:
tangent is the ratio sine/cosine
So to compute something like tan(11pi/6), you'll divide the values sin(11pi/6) over cos(11pi/6).


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With all that in mind you should get these answers


sin(2pi/3) = <font color=red>sqrt(3)/2</font>
cos(3pi/4) = <font color=red>-sqrt(2)/2</font>
tan(5pi/6) = <font color=red>-sqrt(3)/3</font>
sin(7pi/6) = <font color=red>-1/2</font>
cos(5pi/4) = <font color=red>-sqrt(2)/2</font>


tan(4pi/3) = <font color=red>sqrt(3)</font>
sin(5pi/3) = <font color=red>-sqrt(3)/2</font>
cos(7pi/4) = <font color=red>sqrt(2)/2</font>
tan(11pi/6) = <font color=red>-sqrt(3)/3</font>


Please let me know if you have a specific question about how to arrive at any one of these answers. 


One way to verify the answers is to use WolframAlpha. GeoGebra is another useful option (you'll need to use the CAS tool). There are many other ways to verify.
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