Understanding Engineering Mathematics

CB

A

q

Figure 6.2

AB

AC

=sinθ(sine ofθ)

AC

AB

=cosecθ(cosecant ofθ)=

1

sinθ

BC

AC

=cosθ(cosine ofθ)

AC

BC

=secθ(secant ofθ)=

1

cosθ

AB

BC

=tanθ(tangent ofθ)

BC

AB

=cotθ(cotangent ofθ)=

1

tanθ

Note that tanθ=

sinθ

cosθ

.
Treatingθas an independent variable, these might also be regarded astrigonometric
functions(90
➤
)ofθ. For general angles, greater than 90°the sign of each ratio depends
on the quadrant it is in – an example in the second quadrant is shown in Figure 6.3.

2nd quadrant 1st quadrant

3rd quadrant 4th quadrant

x

r

y

P

q

y

x

Figure 6.3General angles.

sinθ=

y

r

=

NP

OP

cosθ=

x

r

=

−ON

OP

tanθ=

y

x

=

NP

−ON

wherer=OP=

√
x^2 +y^2 >0,ONandNPare the positive lengths indicated andx,y
are the coordinates ofP, including appropriate signs.θis measured anticlockwise – the