## SAT SUBJECT TEST MATH LEVEL 2

## PART 2

## REVIEW OF MAJOR TOPICS

## CHAPTER 1

Functions

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1.3 Trigonometric Functions and Their Inverses

### DEFINITIONS

The general definitions of the six trigonometric functions are obtained from an angle placed in standard position on a rectangular coordinate system. When an angle is placed so that its vertex is at the origin, its initial side is along the positive *x*-axis, and its terminal side is anywhere on the coordinate system, it is said to be in *standard position*. The angle is given a positive value if it is measured in a counterclockwise direction from the initial side to the terminal side, and a negative value if it is measured in a clockwise direction.

Let *P(x,y*) be any point on the terminal side of the angle, and let *r *represent the distance between *O *and *P*. The six trigonometric functions are defined to be:

sin θ and cos θ are always between –1 and 1. |

From these definitions it follows that:

The distance *OP *is always positive, and the *x *and *y *coordinates of *P *are positive or negative depending on which quadrant the terminal side of lies in. The signs of the trigonometric functions are indicated in the following table.

Just remember: |

Each angle whose terminal side lies in quadrant II, III, or IV has associated with it an angle called its *reference angle *, which is formed by the *x*-axis and the terminal side.

Any trig function of = ± the same function of . The sign is determined by the quadrant in which the terminal side lies.

**EXAMPLES**

**1. Express sin 320° in terms of** .

Since the sine is negative in quadrant IV, sin 320° = –sin 40°.

**2. Express cot 200° in terms of** .

Since the cotangent is positive in quadrant III, cot 200° = cot 20°.

**3. Express cos 130° in terms of** .

Since the cosine is negative in quadrant II, cos 130° = –cos 50°.

Sine and cosine, tangent and cotangent, and secant and cosecant are *cofunction pairs*. *Cofunctions of complementary angles are equal. *If and are complementary, then trig () = cotrig () and trig () = cotrig () .

**4. If both the angles are acute and sin (3 x + 20°) = cos (2x – 40°), find x.**

Since these cofunctions are equal, the angles must be complementary.

Therefore,

**EXERCISES**

1. Express cos 320° as a function of an angle between 0° and 90°.

(A) cos 40°

(B) sin 40°

(C) cos 50°

(D) sin 50°

(E) none of the above

2. If point *P*(–5,12) lies on the terminal side of in standard position, sin =

(A)

(B)

(C)

(D)

(E)

3. If and sin , then tan =

(A)

(B)

(C)

(D)

(E) none of the above

4. If *x *is an angle in quadrant III and tan (*x *– 30°) = cot *x*, find *x*.

(A) 240°

(B) 225°

(C) 210°

(D) 60°

(E) none of the above

5. If 90° < < 180° and 270° < < 360°, then which of the following *cannot *be true?

(A) sin = sin

(B) tan = sin

(C) tan = tan

(D) sin = cos

(E) sec = csc

6. Expressed as a function of an acute angle, cos 310° + cos 190° =

(A) –cos 40°

(B) cos 70°

(C) –cos 50°

(D) sin 20°

(E) –cos 70°