Rationalizing the denominator of a radical expression
Rationalize the denominator and simplify
We can rewrite the expression using the quotient property for square roots.
To rationalize the denominator means to rewrite the fraction without a radical in
th
Trigonometry
Chapter 1 Angles and their measure
Exercises: Draw each angle (in standard position; initial ray
on the positive .
1 . 30
2. 120
3. 450
Converting from degrees to radians
=
.
180 deg
Exercises: Convert from degrees to radians
1. 120 2. 240
WEEK 5
CHAPTER 9
TRIGONOMETRY
Angles are measured in degrees or radians.
One revolution = 360
Radian Measure:
Definition: One radian is the magnitude of the angle at the centre of the circle subtended by an arc equal
in length to the radius of the circle.
TRIG LEVELING SKETCH AND CALCULATION
Z = measured zenith angle
S = measured slope distance
V = S * Cos Z
apparent target
r = refraction
Hb= Target H.
S
V
B
Z
c
Ha. (Inst. Height)
A
Bench Mark Elev.
Elevation Datum (NGVD/NAVD)
Size of Curvature and Refract
Rationalizing the denominator of a radical expression using
conjugates
Rationalize the denominator and simplify
To rationalize the denominator is to write an equivalent fraction without radicals
in the denominator.
To do this, we'll multiply the numerator
.
Determining whether two
functions are inverses of
each other
For each pair of functions
and
below,
find
d
an
.
Then, determine whether
and
are inverses of each
other.
Simplify your answers as much
as possible.
(Assume that your expressions
are defined f