Solving Simpson's Rule: Finding cos^2(1^2)

In summary: Your calculator is likely in degree mode, so when you input cos(1^2), it is taking the cosine of 1 degree squared, not 1 radian squared. This is why you are getting a different answer. To obtain the correct answer of 0.2919, make sure your calculator is in radian mode before inputting the expression. In summary, when using a calculator to find the answer to cos^2(1^2), make sure it is in radian mode to obtain the correct answer of 0.2919.
  • #1
Jeviah
16
0

Homework Statement


hello, I'm currently studying simpsons rule (unrelated) however the method requires the answer to cos^2(1^2) the answer given by my tutor is 0.2919, I have been unable to get this answer after inputting cos in various ways I always get 0.9997, which is right and if 0.2919 is correct how do I obtain it using a calculator?

Homework Equations


N/A

The Attempt at a Solution


have attempted this by inputting the following into my calculator:
(cos(1^2))^2
cos(1^2)*cos(1^2)
cos(1^2)^2

The answer is never 0.2919
 
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  • #2
Jeviah said:

Homework Statement


hello, I'm currently studying simpsons rule (unrelated) however the method requires the answer to cos^2(1^2) the answer given by my tutor is 0.2919, I have been unable to get this answer after inputting cos in various ways I always get 0.9997, which is right and if 0.2919 is correct how do I obtain it using a calculator?

Homework Equations


N/A

The Attempt at a Solution


have attempted this by inputting the following into my calculator:
(cos(1^2))^2
cos(1^2)*cos(1^2)
cos(1^2)^2

The answer is never 0.2919
Its about degree-radian convention.
 
  • #3
Jeviah said:
have attempted this by inputting the following into my calculator:
(cos(1^2))^2
cos(1^2)*cos(1^2)
cos(1^2)^2

The answer is never 0.2919
Your calculator is in degree mode. In radian mode I get approximately .2919.
BTW, why bother with 1^2, since 1^2 = 1?

Arman777 said:
Its about degree-radian convention.
Exactly
 

What is Simpson's Rule and how is it used?

Simpson's Rule is a method for approximating the area under a curve using a polynomial function. It is used to find the numerical value of integrals, which can be difficult or impossible to solve analytically.

What is the formula for Simpson's Rule?

The formula for Simpson's Rule is:
S = (b-a)/6 * [f(a) + 4f((a+b)/2) + f(b)]
where S is the approximate area, a and b are the lower and upper limits of integration, and f(x) is the function being integrated.

How do you use Simpson's Rule to find cos^2(1^2)?

To use Simpson's Rule to find cos^2(1^2), we first need to express the function in the form of a polynomial. In this case, cos^2(1^2) can be rewritten as (cos(x))^2. Then, we can use the formula for Simpson's Rule to approximate the area under the curve of the polynomial function for a given interval of x values.

What is the significance of the number 1^2 in cos^2(1^2)?

The number 1^2 in cos^2(1^2) represents the upper limit of integration for the function. In other words, we are finding the area under the curve of the function cos^2(x) from x=0 to x=1.

Can Simpson's Rule be used to find the exact value of cos^2(1^2)?

No, Simpson's Rule can only provide an approximation of the area under the curve. To find the exact value of cos^2(1^2), we would need to solve the integral analytically or use another method of numerical integration.

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