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

116 Chapter 3 The trigonometric functions
3.2 DEGREESANDRADIANS
Angles can be measured in units of either degrees or radians. The symbol for degree
is ◦ . Usually no symbol is used to denote radians and this is the convention adopted in
this book.
A complete revolution is defined as 360 ◦ or 2π radians. It is easy to use this fact to
convert between the two measures. We have
Note that
360 ◦ = 2π radians
1 ◦ = 2π
360 = π
180 radians
1 radian = 180
π
π
radians = 90◦
2
3π
2
π radians = 180 ◦
radians = 270◦
degrees ≈ 57.3◦
Yourcalculatorshouldbeabletoworkwithanglesmeasuredinbothradiansanddegrees.
Usually the Mode button allows you toselect the appropriate measure.
3.3 THETRIGONOMETRICRATIOS
Considertheangle θ intheright-angledtriangleABC,asshowninFigure3.1.Wedefine
the trigonometricratiossine, cosineandtangent asfollows:
sinθ=
cosθ=
tanθ=
sideopposite toangle
hypotenuse
sideadjacent toangle
hypotenuse
= BC
AC
= AB
AC
sideopposite toangle
sideadjacent toangle = BC
AB
C
a
A
u
B
Figure3.1
A right-angled triangle, ABC.