Review the following concepts if needed:** **

- Logarithms for Physics Help
- Exponential Functions for Physics Help
- Trigonometric Functions for Physics Help
- Trigonometric Identities for Physics Help

**Logarithms, Exponentials, And Trigonometry Practice Test**

1. The range of the common logarithm function extends over the set of

(a) all real numbers.

(b) all the positive real numbers.

(c) all the nonnegative real numbers.

(d) all real numbers except zero.

2. From a distance of 503 meters, a spherical satellite has an angular diameter (that is, its disk subtends an observed angle) of 2.00 degrees of arc. What is the actual radius of the satellite? Assume that the distance is measured from the center of the satellite.

(a) 8.78 meters

(b) 17.6 meters

(c) 10.6 meters

(d) 2.79 meters

3. What is sin 45°? Do not use a calculator to determine the answer. Use the Pythagorean theorem (as defined in Chapter 4) and simple algebra.

(a) 2 ^{1/2}

(b) 2 ^{−1/2}

(c) 1

(d) It cannot be determined from this information.

4. The natural logarithm of −5.670, to four significant figures, is equal to

(a) 1.735.

(b) −1.735.

(c) 0.7536.

(d) Nothing; the value is not defined.

5. What is the value of the quotient (10 ^{(4.553)} /10 ^{(3.553)} )? Parentheses have been added to make the meaning of this expression completely clear.

(a) 10

(b) 1

(c) 4.553

(d) 3.553

6. Suppose that you are given the equation *e ^{x}* = −5 and told to solve it. What can you say right away about the value of

*x?*

(a) It is a large positive real number.

(b) It is between 0 and 1.

(c) It is a real number and is large negatively.

(d) It is not a real number.

7. What is In *e* to three significant figures? Use a calculator if you need it.

(a) 0.434

(b) 2.718

(c) 1.000

(d) It can’t be figured out without more information.

8. Suppose that the cosine of a small angle is 0.950. What is the cosine of the negative of that angle—that is, the cosine of the same angle measured clockwise rather than counterclockwise?

(a) 0.950

(b) −0.950

(c) 0.050

(d) −0.050

9. Given that the length of a day on earth is 24 hours (as measured with respect to the sun), how many degrees of arc does the earth rotate through in 1 minute of time?

(a) 1/60

(b) 15

(c) 1/3,600

(d) 0.25

10. Suppose that two points on the earth’s equator are separated by one second of arc (that is, 1/3,600 of an angular degree). If the circumference of the earth at the equator is given as 4.00 × 10 ^{7} meters, how far apart are these two points?

(a) 1.11 × 10 ^{4} meters

(b) 463 meters

(c) 30.9 meters

(d) It cannot be calculated from this information.

**Answers:**

1. a

2. a

3. b

4. d

5. a

6. d

7. c

8. a

9. d

10. c

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