Hyperbolic Functions Practice Test

Review the following concepts if needed:

• The 6 Hyperbolic Functions Help
• Hyperbolic Inverses Help
• Hyperbolic Function Facts Help

Hyperbolic Functions Practice Test

A good score is eight correct.

1. Suppose we know that the hyperbolic cosine of a certain variable is equal to 1. What is the hyperbolic cosine of twice that variable?

(a) 1

(b) 0

(c) e ^–1

(d) e

2. From the logarithm formulas, it is apparent that the hyperbolic arctangent of 1 is

(a) equal to e

(b) equal to 1/e

(c) equal to 0

(d) not defined

3. The number e is equal to the ratio of

(a) a circle’s area to its radius

(b) a circle’s diameter to its radius

(c) two large negative integers

(d) no two whole numbers

4. As the value of x becomes larger without limit, the value of cosh x

(a) also becomes larger without limit

(b) approaches zero

(c) approaches 1

(d) becomes larger without limit, negatively

5. How is the hyperbolic secant of 10 related to the hyperbolic secant of –10?

(a) They are reciprocals

(b) They add up to zero

(c) Their ratio is equal to e

(d) They are the same

6. A unit hyperbola can be represented by the equation

(a) x ² = 1 + y ²

(b) x ² + y ² = 1

(c) y = 1 – x ²

(d) y = 1 + x ²

7. A simpler way to express e to the power of arcsech x is

(a) non-existent because such an expression is too complicated to deal with

(b) x ^–1 + ( x ^–2 – 1) ^1/2

(c) x ^–1 + ( x ^–2 + 1) ^1/2

(d) x ^–1 – ( x ^–2 – 1) ^1/2

8. As the value of x increases without limit, what happens to the value of e ^{– x} ?

(a) It becomes larger and larger, positively

(b) It stays the same

(c) It approaches zero

(d) It becomes larger and larger, negatively

9. The hyperbolic tangent is equivalent to

(a) the reciprocal of the hyperbolic sine

(b) the ratio of the hyperbolic sine to the hyperbolic cosine

(c) the reciprocal of the circular sine

(d) the ratio of the circular sine to the circular cosine

10. Using the exponential formulas, the hyperbolic sine of 3 is expressed as

(a) (e ³ – e ^–3 )/2

(b) 2/(e ³ – e ^–3 )

(c) (e ³ + e ^–3 )/2

(d) any of the above

Answers:

1. a

2. d

3. d

4. a

5. d

6. a

7. b

8. c

9. b

10. a