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

Write algorithm for the multiplication of a 3-digit number, E1) Why do we s...

E1) Why do we shift the place by one, of the result in the second row of the calculation, when we multiply, say, 35 by 237 E2) Write down the algorithm for the multiplication of

Compute the total and annual return on the investment, 1. Calculate the ann...

1. Calculate the annual interest that you will receive on the described bond-A $500 Treasury bond with a current yield of 4 .2% that is quoted at 106 points? 2. Compute the tota

Relation between hieght, volume=(1/3)(pi)(radius of base)2(height) curved ...

volume=(1/3)(pi)(radius of base)2(height) curved surface area=(pi)(r)(l), r is radius of base and l is length of straight line connecting apex of cone with point on edge of base

System of differential equations for the population, Write down the system ...

Write down the system of differential equations for the population of both predators and prey by using the assumptions above. Solution We will start off through letting that

Practical geometry, Ask question draw a line parallel to given line xy at a...

Ask question draw a line parallel to given line xy at a distance of 5cm from it #Minimum 100 words accepted#

Exponential smoothing, Exponential smoothing It is a weighted moving a...

Exponential smoothing It is a weighted moving average technique, this is described by: New forecast = Old forecast + a (Latest Observation - Old forecast) Whereas a = Sm

Create a guessing game for children to teaching maths, E1) Create a guessin...

E1) Create a guessing game for children of Class 2, to familiarise them with the concept of a time interval E2) How could you use group dancing to teach concepts of geometry? Th

Solve the value of x and y , 7(y + 3) - 2(x + 2) = 14, 4 (y - 2) + 3(x ...

7(y + 3) - 2(x + 2) = 14, 4 (y - 2) + 3(x - 3) = 2 Ans:    7(y + 3) - 2 (x+ 2) = 14          --------- (1) 4(y- 2) + 3(x - 3) = 2 ----------(2) From (1) 7y +21 -

Geometry, how do you do rotations

how do you do rotations

If pth term of ap is q and qth term is p. p.t its nth term, If the p th te...

If the p th term of an AP is q and the q th term is p. P.T its n th term is (p+q-n). Ans:    APQ a p = q a q = p a n = ? a + (p-1) d = q a + (q-1) d = p

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