## SAT SUBJECT TEST MATH LEVEL 2

## PART 2

## REVIEW OF MAJOR TOPICS

## CHAPTER 1

Functions

###

1.3 Trigonometric Functions and Their Inverses

### ARCS AND ANGLES

Although the degree is the chief unit used to measure an angle in elementary mathematics courses, the radian has several advantages in more advanced mathematics. A radian is one radius length. The circle shown in the figure below has radius *r*. The circumference of this circle is 360°, or 2π radians, so one radian is .

**EXAMPLES**

**1. In each of the following, convert the degrees to radians or the radians to degrees.** (If no unit of measurement is indicated, radians are assumed.)

**(A)** 30°

**(B)** 270°

**(C)**

**(D)**

**(E)** 24

Although is optional.^{R } |

**SOLUTIONS**

**(A)** To change degrees to radians multiply by , so 30° = 30° .

**(B)** 270°

**(C)** To change radians to degrees, multiply by , so

**(D)**

**(E)**

In a circle of radius *r *inches with an arc subtended by a central angle of measured in radians, two important formulas can be derived. The length of the arc, *s*, is equal to *r*, and the area of the sector, *AOB*, is equal to .

**2. Find the area of the sector and the length of the arc subtended by a central angle of** **radians in a circle whose radius is 6 inches.**

**3. In a circle of radius 8 inches, find the area of the sector whose arc length is 6**π **inches.**

**4. Find the length of the radius of a circle in which a central angle of 60° subtends an arc of length 8π inches.**

The 60° angle must be converted to radians:

60° = 60° radians = radians

Therefore,

**EXERCISES**

1. An angle of 30 radians is equal to how many degrees?

(A)

(B)

(C)

(D)

(E)

2. If a sector of a circle has an arc length of 2π inches and an area of 6π square inches, what is the length of the radius of the circle?

(A) 1

(B) 2

(C) 3

(D) 6

(E) 12

3. If a circle has a circumference of 16 inches, the area of a sector with a central angle of 4.7 radians is

(A) 10

(B) 12

(C) 15

(D) 25

(E) 48

4. A central angle of 40° in a circle of radius 1 inch intercepts an arc whose length is *s*. Find *s*.

(A) 0.7

(B) 1.4

(C) 2.0

(D) 3.0

(E) 40

5. The pendulum on a clock swings through an angle of 25°, and the tip sweeps out an arc of 12 inches. How long is the pendulum?

(A) 1.67 inches

(B) 13.8 inches

(C) 27.5 inches

(D) 43.2 inches

(E) 86.4 inches