﻿ ﻿ARCS AND ANGLES - Trigonometric Functions and Their Inverses - Functions - REVIEW OF MAJOR TOPICS - SAT SUBJECT TEST MATH LEVEL 2

## PART 2 ## REVIEW OF MAJOR TOPICS ## CHAPTER 1Functions

### 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

 TIP Although R is used to indicate radians, a radian actually has no units, so the use of R is optional.

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 6π 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

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