Evaluate following sin 2 ?/3   and sin (-2 ?/3)

Solution: The first evaluation in this part uses the angle 2 ?/3.  It is not on our unit circle above, though notice that  2 ?/3= ? - ?/3 .  thus 2 ?/3 is found through rotating up from the -ve  x-axis.

It means that the line for 2 ?/3 will be a mirror image of the line for ?/3 only within the second quadrant. The coordinates for 2 ?/3   will be the coordinates for ?/3 except the x coordinate will be negative.

Similarly for - 2 ?/3 we can notice that - 2 ?/3  = - ?+  ?/3   , hence this angle can be found by rotating down ?/3   from the -ve x-axis. It means that the line for ?/3  will be a mirror image of- 2 ?/3 the line for ?/3  only in the third quadrant and the coordinates will be the same as the coordinates for ?/3  except both will be negative.

Both of these angles along with their coordinates are illustrated on the following unit circle.

From this unit circle we can see that sin ( 2 ?/3  ) =√3/2 and sin ( -2 ?/3  )=√3/2

It leads to a nice fact regarding the sine function. The sine function is known an odd function and hence for any angle we have

                                          sin ( - θ ) = - sin (θ )

Posted Date: 4/11/2013 2:24:28 AM | Location : United States

Ask an Expert

Related Discussions:- Evaluate following unit circle, Assignment Help, Ask Question on Evaluate following unit circle, Get Answer, Expert's Help, Evaluate following unit circle Discussions

Write discussion on Evaluate following unit circle
Your posts are moderated

Write your message here..

Related Questions

Sequence and series, how can we prove that an absolute convergent series is... how can we prove that an absolute convergent series is convergent but the converse is not true.

Laws of logarithms, express each logariths in terms of log3 P and log3 Q. 1... express each logariths in terms of log3 P and log3 Q. 1. log3 P^2 Q^3

Percents, write as a percent 6/10 write as a percent 6/10

Column method, 26 + 34= 26 + 34=

Lines- common polar coordinate graphs, Lines- Common Polar Coordinate Graph... Lines- Common Polar Coordinate Graphs A few lines have quite simple equations in polar coordinates. 1.  θ = β We are able to see that this is a line by converting to Car

Properties of cross product - vector, Properties of Cross product If u,... Properties of Cross product If u, v and w are vectors and c is a number then u → * v → = -v → * w →                                                       (cu → ) * v → =

Tests for relative minimum, Tests for relative minimum For a relative ... Tests for relative minimum For a relative minimum point there are two tests: i.The first derivative, which is (dy)/(dx)  = f´(x) = 0 ii.The second derivative, which i

How much more does she required to sell to meet her goal, Hanna's sales tar... Hanna's sales target for the week is $5,000. So far she has sold $3,574.38 worth of merchandise. How much more does she required to sell to meet her goal? You must ?nd out the

Write down those features of such interactions, After seeing some children ... After seeing some children interacting naturally, write down those features of such interactions that make peer learning potentially a better way of learning. Another point that

Calculate probability, The following table contains some information about... The following table contains some information about the model used. Assume the probabilities given by the model are those of being a good writer. Variable