082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

3.3 The trigonometric ratios 119
y
y
B
P
P
B
u
u
O A x
A
O
x
First quadrant
y
Second quadrant
y
A
O
u
x
O
u
A
x
P
B
B
P
Third quadrant
Fourth quadrant
Figure3.4
Evaluating the trigonometric ratios in each ofthe fourquadrants.
So,for example,
sin(8.76) = sin(8.76 −2π) = sin(2.477) = 0.617
cos(14.5) = cos(14.5 −4π) = cos(1.934) = −0.355
Negative angles are interpreted as a clockwise movement of the arm. Figure 3.6 illustrates
an angle of −2. Note that
sin(−2) = sin(2π −2) = sin(4.283) = −0.909
sinceananticlockwise movement ofOPof4.283radians would resultinthe armbeing
inthe same position as a clockwise movement of 2 radians.
y
sin u > 0
cos u < 0
tan u < 0
sin u > 0
cos u > 0
tan u > 0
y
sin u < 0
cos u < 0
tan u > 0
sin u < 0
cos u > 0
tan u < 0
x
O
u = –2
x
Figure3.5
Sign ofthe trigonometric ratios in
each ofthe four quadrants.
P
Figure3.6
Illustrationofthe angle θ = −2.