POINT

P

HYPOTENUSE

(RADIUS)

r

(SIDE

OPPOSITE 0 )

y

RIGHT

0

ANGLE

x

(SIDE ADJACENT TO 0 )

y

length of the opposite side

sin 0 = =

r

length of the hypotenuse

x

length of the adjacent side

cos 0 =

=

r

length of the hypotenuse

y

lengthof the opposite side

tan 0 =

=

x

length of the adjacent side

DCf1201

1

1

0.5

0.5

0

0

o

o

o

o

270

180 o

o

360

o

o

270

60

180 o

360

o

60

90

90

0 (DEGREES)

0 (DEGREES)

-1

-1

DCf1203

DCf1203

The tangent of the angle θ is the ratio of the side

The cosine is the ratio expressed by dividing the

side adjacent to the angle θ by the hypotenuse.

opposite the angle θ to the side adjacent. Again,

Therefore, referring to figure 12-1:

referring to figure 12-1:

In contrast to the sine, the cosine decreases as the

angle θ becomes larger. This relationship between the

value of the cosine and the size of the angle is shown by

There are certain principles of physics that you

the cosine curve shown in figure 12-3. At 0° the cosine

n e e d t o k n ow i n o r d e r t o h ave a n a d e q u a t e

equals one; at 90° the cosine equals zero; and at 60° the

cosine is half the value of the cosine at 0°.

understanding of stability. You should be familiar with

12-2