Hyperbolic functions and identities Quiz

1. Which statement about $\cosh x$ is true?

• A. It is odd
• B. Its range is all real numbers
• C. Its minimum value is $1$ at $x=0$
• D. It has asymptotes $y=\pm1$

2. Which is a correct identity?

• A. $\cosh^2x+\sinh^2x=1$
• B. $\cosh^2x-\sinh^2x=1$
• C. $\sinh^2x-\cosh^2x=1$
• D. $\cosh2x=\cosh^2x-\sinh^2x$

3. Given $\sinh x=\frac34$, the value of $\cosh x$ is

• A. $\frac74$
• B. $\frac{\sqrt7}{4}$
• C. $1$
• D. $\frac{5}{4}$

4. Solving $\cosh x=\frac12$ for real $x$ gives

• A. $x=\ln2$
• B. $x=0$
• C. $x=\pm\ln2$
• D. No real solution

5. $\sinh x+\cosh x$ is equal to

• A. $e^x$
• B. $e^{-x}$
• C. $2e^x$
• D. $\sinh2x$