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

Shares and divident, A man invest ?13500 partly in shares paying 6% at ?140...

A man invest ?13500 partly in shares paying 6% at ?140 and partly in 5% at 125.If he is tolal income is 560, how much has he invested in each?

What was his weight within pounds and ounces, Justin weighed 8 lb 12 oz whi...

Justin weighed 8 lb 12 oz while he was born. At his two-week check-up, he had gained 8 ounces. What was his weight within pounds and ounces? There are 16 ounces within a pound.

Operation research, difference between scope and application of operation r...

difference between scope and application of operation research

Assisnment, How a student of mathematics of b.sc can make an assignment on...

How a student of mathematics of b.sc can make an assignment on topic of asymptotes?

Solid, The lateral edge of a pyramidal church spire is 61feet.Each side of ...

The lateral edge of a pyramidal church spire is 61feet.Each side of its octagonal base is 22feet. What will be the cost of painting the spire at 2.5 cents a square foot

How many hours will it take for them to be 822 miles apart, Two trains leav...

Two trains leave the same city at the same time, one going east and the other going west. If one train is traveling at 65 mph and the other at 72 mph, how many hours will it take f

Linear graph, in the form of linear graph interpret the ralationship betwee...

in the form of linear graph interpret the ralationship between two quantities

Cooking measurement question, Ask question what is half of 1 1/3 liquid mea...

Ask question what is half of 1 1/3 liquid measurements?

Volume and surface area, a conical hole drilled in a circular cylinder of h...

a conical hole drilled in a circular cylinder of height 12 and radius 5cm the height and radius of cone are also same find volume

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