Inverse cosine, Mathematics

Assignment Help:

Inverse Cosine : Now see at inverse cosine.  Following is the definition for the inverse cosine.

                        y = cos-1 x       ⇔ cos y = x                   for     0 ≤ y ≤ ?

As with the inverse since we've got a restriction on the angles, y, which we get out of the inverse cosine function. Again, if you'd like to verify it a quick sketch of unit circle should convince you that this range will cover all possible values of cosine exactly once.  Also, we have

                          -1 ≤ x ≤ 1 because -1 ≤ cos ( y ) ≤ 1.

Example   Evaluate cos-1   (-√2/  2)

Solution : As with the inverse sine we are actually just asking the following.

                                                       cos y = - √2 /2

where y have to meet the requirements given above.  From a unit circle we can illustrates that we must have y =3 ∏/4    .

The inverse cosine & cosine functions are also inverses of each other and therefore we have,

cos (cos-1  x ) = x                                          cos-1 (cos x ) =x

To determine the derivative we'll do the similar kind of work which we did with the inverse sine above.  If we begin with then,

                                                     f ( x ) = cos x          g ( x ) = cos-1 x

then

g ′ ( x ) =1/f ′ ( g ( x )) = 1/- sin (cos-1  x )

Here Simplifying the denominator is almost alike to the work we did for the inverse sine & so isn't illustrated here.  Upon simplifying we get the given derivative.

706_inverse cosec.png

Therefore, the derivative of the inverse cosine is closely identical to the derivative of the inverse sine. The single difference is the negative sign.


Related Discussions:- Inverse cosine

Properties of summation notation, Properties Now there are a couple of ...

Properties Now there are a couple of formulas for summation notation. 1. here c is any number. Therefore, we can factor constants out of a summation. 2. T

What is the minimum number of students, Question 1: What is the minimum...

Question 1: What is the minimum number of students each of whom comes from one of the 50 different states, enrolled in a university to guarantee that there are at least 100 who

Karls pearsons co-efficient of correlation, Aim: To test the significan...

Aim: To test the significant relationship between the accounting ratios of operating management and standard ideal ratios. Null Hypothesis(H 0 ) : There is no significa

Geometyr, Lines EF and GH are graphed on this coordinate plane. Which point...

Lines EF and GH are graphed on this coordinate plane. Which point is the intersection of lines EF and GH?

Integrated marketing, #question.Explain its nature and how it influences th...

#question.Explain its nature and how it influences the integrated marketing communications mix and distinguish between tactical and strategic use of integrated marketing communicat

Find the length of the parallelogram, The perimeter of a parallelogram is 5...

The perimeter of a parallelogram is 50 cm. The length of the parallelogram is 5 cm more than the width. Find the length of the parallelogram. Let w = the width of the parallelo

What is the square root of -i, To find sq root by the simple step... root (...

To find sq root by the simple step... root (-i)=a+ib............... and arg of -i= -pi/2 or 5pi/2

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