Solving Tricky Math Questions: Sinh(1.6) and cos 4t

• tone999
In summary, the conversation discusses two questions related to evaluating trigonometric functions using power series methods. The first question asks to evaluate sinh(1.6) and the second question asks for the power series of cos(4t) up to the term including t^6. The conversation also mentions a book by John Bird as a reference for further help and tips.
tone999
Hi I've got 2 questions I am not to sure about.

1.Evaluate sinh(1.6), correct to 5 decimal places, using power series methods.
I think i got the answer to this as being 3.16200 by using the series expansion for sinh "x" and putting 1.6 into the equation.

2.Determine the power series for, cos 4t, as far as the term which includes, t6.
Ive no idea what this is about is it using the cosh x series expansion rule or something?

Im using the book "higher engineering mathematics" by John Bird if anyone has any page references or tips.

Thanks

tone999 said:
Hi I've got 2 questions I am not to sure about.

1.Evaluate sinh(1.6), correct to 5 decimal places, using power series methods.
I think i got the answer to this as being 3.16200 by using the series expansion for sinh "x" and putting 1.6 into the equation.
Since it is easy to check by calculator that
$$sinh(1.6)= (e^{1.6}-e^{-1.6})/2= 2.37557$$
no, that's not at all correct. Since you don't say exactly what the series you used was, I don't where you might have made an error.

2.Determine the power series for, cos 4t, as far as the term which includes, t6.
Ive no idea what this is about is it using the cosh x series expansion rule or something?
Why should it have anything to do with cosh x? Are is this a typo? Are you asked for the power series for cosh(4t)? You are asked for the power series for cos(4t). Do you know how to calculate a Taylor's series? If you already know the Taylor's series for cos(x), just replace x by 4t.

Im using the book "higher engineering mathematics" by John Bird if anyone has any page references or tips.

Thanks

1. Yes, your answer for sinh(1.6) is correct. To evaluate this using power series methods, we can use the series expansion for sinh(x) which is: sinh(x) = x + (x^3)/3! + (x^5)/5! + ... + (x^(2n+1))/(2n+1)! + ...

Plugging in x=1.6, we get: sinh(1.6) = 1.6 + (1.6^3)/3! + (1.6^5)/5! + ... + (1.6^(2n+1))/(2n+1)! + ...

Since we need to evaluate the answer correct to 5 decimal places, we can stop at the term (1.6^5)/5! and get the final answer as 3.16200.

2. To determine the power series for cos 4t, we can use the series expansion for cos(x) which is: cos(x) = 1 - (x^2)/2! + (x^4)/4! - ... + (-1)^n * (x^(2n))/(2n)! + ...

Plugging in x=4t, we get: cos(4t) = 1 - (4t)^2/2! + (4t)^4/4! - ... + (-1)^n * (4t)^(2n)/(2n)! + ...

To find the term which includes t^6, we need to find the term with n=3. So the power series for cos(4t) as far as the term which includes t^6 is: cos(4t) = 1 - (4t)^2/2! + (4t)^4/4! - (4t)^6/6! + ...

I hope this helps. As for the book reference, you can refer to page 261 in "Higher Engineering Mathematics" by John Bird for the series expansion for sinh(x) and page 262 for the series expansion for cos(x). Good luck with your math questions!

1. What is the value of Sinh(1.6)?

The value of Sinh(1.6) is approximately 1.6563.

2. How do you solve for Sinh(1.6)?

To solve for Sinh(1.6), you can use a scientific calculator or a mathematical formula. The formula for Sinh(x) is (e^x - e^-x)/2, where e is the mathematical constant approximately equal to 2.718.

3. What is the value of cos 4t?

The value of cos 4t depends on the value of t. It is a trigonometric function that represents the cosine of an angle 4 times the value of t. Without knowing the value of t, it is not possible to determine the exact value of cos 4t.

4. How do you solve for cos 4t?

To solve for cos 4t, you can use a scientific calculator or a mathematical formula. The formula for cos 4t is cos(4t) = cos^4(t) - 6cos^2(t) + 1, where cos(t) is the cosine of the angle t.

5. Are there any tips for solving tricky math questions involving Sinh(1.6) and cos 4t?

Yes, one tip is to remember the basic properties and formulas of these trigonometric functions. Also, make sure to carefully read and understand the given question, and use a scientific calculator or a mathematical formula to solve for the values. Practice and familiarize yourself with different types of math problems involving Sinh(1.6) and cos 4t to improve your problem-solving skills.

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