Each of Exercises 1–4 gives a value of sinh x or cosh x. Use t...

Question

Each of Exercises 1–4 gives a value of sinh x or cosh x. Use the definitions and the identity cosh²x - sinh²x = 1 to find the values of the remaining five hyperbolic functions.

4. cosh x = 13/5, x>0

Accepted Answer

Welcome back, everyone. Given o X equals 13 divided by 12 and X is greater than 0, find the remaining 5 hyperbolic function values. For this problem, let's understand that the remaining 5 hyperbolic functions would be cinch X. 0 X. Sash X Cosa X And finally, cough X. So these are the 5 remaining hyperbolic functions that we want to find. Let's begin with singe, and what we can do is simply remember the identity. Cash squared X minus singe squared X is equal to 1. We can rearrange this expression to show that sing squared X is equal to. Caus square x minus 1 and we can take square root of both sides to show that cinch X is equal to positive or negative square root of cash. Squared X minus 1. Because X is greater than 0, we have to remember that cinch is positive when X is greater than 0, right? So we're going to take the positive solution, meaning in this case, cinch X is going to be positive square root of cash squared, that's 13 divided by 12 2 minus 1. Now let's square 13 square is 169. In 12 square there's 144. So when we subtract 1, which is 144 divided by 144, We subtract 169 minus 144, that's 25, and the denominator remains the same. We're using the common denominator. So, square root of 25 is 5. And square root of 144 is 12, so we got the value of sin, which is 5 divided by 12, and from here we can easily identify the remaining functions. So tinge X is defined as sin. Divided by cash. We know that cinch is 5 divided by 12, and we're dividing by cash, which is 13 divided by 12. We can cancel out the denominator to get 5 divided by 13. So 10 is 5 divided by 13. What about sesh? Stash X is defined as one divided by cash. So we want to take the reciprocal value of cash, which is 1 divided by 13 divided by 12, and that's basically 12 divided by 13. Now Kosa. Of X is the reciprocal value of sin. So we're going to take 1 and divide it by cinch X or basically 1 divided by 5 divided by 12. Which is 12 divided by 5. And finally, cost is the reciprocal value of change. So we can just flip 5 and 13, right, to get 13 divided by 5 because cost X is equal to 1 divided by 10 X, which in this case is 1 divided by 5 divided by 13, and this is equal to 13 divided by 5. Well, once we have our final answers, and thank you for watching.

Each of Exercises 1–4 gives a value of sinh x or cosh x. Use the definitions and the identity cosh²x - sinh²x = 1 to find the values of the remaining five hyperbolic functions.4. cosh x = 13/5, x>0

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Each of Exercises 1–4 gives a value of sinh x or cosh x. Use the definitions and the identity cosh²x - sinh²x = 1 to find the values of the remaining five hyperbolic functions.
4. cosh x = 13/5, x>0