Quiz about Hyperbolic functions

Question 1

Find the real value of x for which $$2\cosh2x+4\sinh2x=2.$$

Accepted Answer

0

Answer

1

Answer

-1/3

Answer

$$\frac{\log3}{2}$$

Question 2

If $$x=\sqrt[]{2},$$ find $$\sinh\left(\log x\right)$$

Accepted Answer

$$\frac{1}{2\sqrt[]{2}}$$

Answer

$$\frac{1}{2}$$

Answer

0

Answer

$$\frac{\left(\sqrt[]{2}-1\right)}{2}$$

Question 3

If $$\operatorname{sech}^{-1}\left(\cos heta ight)=x$$ then $$x=?$$

Accepted Answer

$$\log\left( an\left(\frac{\pi}{4}+\frac{ heta}{2} ight) ight)$$

Answer

$$\log\left(\cot\frac{ heta}{2} ight)$$

Answer

$$\log\left( an\frac{ heta}{2} ight)$$

Answer

$$\log\left(\cot\left(\frac{\pi}{4}+\frac{ heta}{2} ight) ight)$$

Question 4

If $$\cos^{-1}\left(u+iv\right)=\alpha+i\beta$$ then

Accepted Answer

$$\frac{u^2}{\cos^2\alpha}-\frac{v^2}{\sin^2\alpha}=1$$

Answer

$$\frac{u^2}{\cos^2\alpha}+\frac{v^2}{\sin^2\alpha}=1$$

Answer

$$\frac{u^2}{\cos^2\beta}-\frac{v^2}{\sin^2\beta}=1$$

Answer

$$\frac{u^2}{\cos^2\beta}+\frac{v^2}{\sin^2\beta}=1$$

Question 5

$$1-\coth^2x=\operatorname{cosech}^2x$$

Accepted Answer

False

Answer

True

Question 6

$$ anh\left(\log\sqrt[]{5} ight)=$$

Accepted Answer

2/3

Answer

3/2

Answer

-2/3

Answer

1/3

Question 7

If $$ anh x=\frac{4}{5}$$ then $$\sinh2x\ $$ is

Accepted Answer

40/9

Answer

40

Answer

80/9

Answer

9

Question 8

If $$\cosh^{-1}\left(\sec heta ight)=x\ $$ then $$e^x$$ is

Accepted Answer

$$\sec heta+ an heta$$

Answer

$$\log\left(\sec heta+ an heta ight)$$

Answer

$$\operatorname{cosec} heta+\cot heta$$

Answer

$$\log\left(\operatorname{cosec} heta+\cot heta ight)$$

Question 9

If $$\cosh u=\sec heta$$ then

Accepted Answer

$$\sinh u= an heta$$

Answer

$$\sinh u=\cot heta$$

Answer

$$\cosh u= an heta$$

Answer

$$\cosh u=\cot heta$$

Question 10

$$\sinh^4x=$$

Accepted Answer

$$\frac{1}{8}\left(\cosh4x-4\cosh2x+3\right)$$

Answer

$$\cosh4x-4\cosh2x+3$$

Answer

$$\frac{1}{16}\left(\cosh4x-4\cosh2x+3\right)$$

Answer

$$\frac{1}{8}\left(\cosh4x-4\cosh2x+6\right)$$

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