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.

2. sinh x = 4/3

Accepted Answer

Welcome back, everyone. Given that cinch X equals 3/4, find the values of the remaining 5 hyperbolic functions. For this problem we want to find 5 remaining hyperbolic functions, those would be cash X. Followed by 1 X. Sash X Kosa X And finally, cough. X. So let's begin. We're going to begin by finding cache X because if we have it, we can identify the remaining ones easily. And we're going to use the identity. Cash squared x minus sing. Squared X equals 1. So if we rearrange, we're going to get ca X equals positive or negative square root of One plus cent. Squared X. And we're going to take the positive route because cache X is always greater than or equal to 1, right? So we only have one possible solution. So cache X is going to be square root of. 1 + 3/4 squared. Let's square 3/4, we get 9 divided by 16. We can use the common denominator of 16. To get 16 + 9. In the numerator, and that's 25, which is divided by 16. Taking square root of each number, we get 5 divided by 4, and this is how we get cash. So, cache access 5 words. Now ci X is simply the ratio between cinch X. And cash X. We know cie is 3/4s, so we're going to divide that by cash, which is 5/4s. Canceling out the 4, we get 3/5. So 1 is 3/5. Now Sesh Is defined as a one divided by cash. So we take the reciprocal value of cash, which is a 1 divided by 5 divided by 4, and that's 4/5. Or cosash. That's the reciprocal of. Sing X and we're going to take 1 divided by 3/4s. Which is 4/3. And finally, We can identify c X by taking the reciprocal value of tinge. So 1 divided by 10, which is 1 divided by 3/5. And that's 5/3. Well done, we have identified the remaining 5 hyperbolic functions. Let's label the 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.2. sinh x = 4/3

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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.
2. sinh x = 4/3