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

Find out the area of the region, Find out the area of the region enclosed b...

Find out the area of the region enclosed by y = x 2 & y =√x . Solution Firstly, just what do we mean by "area enclosed by". This means that the region we're interested in

Surds and logarithms, what are these all about and could i have some exampl...

what are these all about and could i have some examples of them please

Give an example of numerator and denominator, Give an example of Numerator ...

Give an example of Numerator and Denominator? Fractions represent parts of a whole object. Fractions are written using a horizontal line, with one number on top of the line and

Commercial arithmetic, if oranges are bought at the rate of 11 for rupees ...

if oranges are bought at the rate of 11 for rupees 10 and are sold at the rate of 10 for rupees 11, find the profit percent

Math, what is quantity ?

what is quantity ?

Laura paid $17 for jeans what was original price of jeans, Laura paid $17 f...

Laura paid $17 for a pair of jeans. The ticketed price was 20% off the original price plus the sign on the rack said, "Take an additional 15% off the ticketed price." What was the

ALJEBRA, HOW TO FIND 2SQUARE *7 CUBE

HOW TO FIND 2SQUARE *7 CUBE

Tests for an ideal index number, Tests for an Ideal Index Number 1. F...

Tests for an Ideal Index Number 1. Factor Reversal Test Factor Reversal Test indicates that when the price index is multiplied along with a quantity index that is factors

Explain binomial distribution, Q. Explain Binomial Distribution? Ans. ...

Q. Explain Binomial Distribution? Ans. The binomial distribution occurs when you are considering the probability function of a binomial experiment. Binomial Experiment

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