Evaluate following unit circle, Mathematics

Assignment Help:

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.

2251_unit circle point.png

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 )


Related Discussions:- Evaluate following unit circle

Average function value of even and odd function, Average Function Value ...

Average Function Value The first application of integrals which we'll see is the average value of a function. The given fact tells us how to calculate this. Average Functi

., Two boys A and B are at two diametrically opposite points on a circle. A...

Two boys A and B are at two diametrically opposite points on a circle. At one instant the two start running on the circle; A anticlockwise with constant speed v and B clockwise wit

Find out how much acid solution mixed, A chemist has one solution which is ...

A chemist has one solution which is 50% acid and a second which is 25% acid. How much of each should be mixed to make 10 litres of 40% acid solution.

Example of fraction, Example  Reduce 24/36 to its lowest terms. 2...

Example  Reduce 24/36 to its lowest terms. 24/36=12/18=6/9=2/3. In the first step we divide the numerator and the denominator by 2. The fraction gets reduced

Inverse laplace transforms, Determining the Laplace transform of a function...

Determining the Laplace transform of a function is not terribly hard if we've found a table of transforms opposite us to use as we saw in the previous section. What we would want t

Differential equation - maple, 1. Consider the following differential equat...

1. Consider the following differential equation with initial conditions: t 2 x'' + 5 t x' + 3 x = 0, x(1) = 3, x'(1) = -13. Assume there is a solution of the form: x (t) = t

Right angle triangle, If the points for a right angle triangle are XYZ wher...

If the points for a right angle triangle are XYZ where do I mark the points?

Commercial, The C.P. of 20 articles is same as theS.P. of x articles.Articl...

The C.P. of 20 articles is same as theS.P. of x articles.Article profit is 25%.Find x

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd