5-3 Solving Trigonometric Equations Worksheet With Answers Page 19
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28of y = tan x cot x is at or below the other graph
other graph when
≤ x ≤
.
when 0 ≤ x < 2π.
5-3 Solving Trigonometric Equations
Therefore,
≤ tan x cot x on 0 ≤ x < 2π.
Therefore, cos x ≤
on
≤ x ≤
.
55.
sin x − 1 < 0
54.
cos x ≤
SOLUTION:
SOLUTION:
sin x − 1. Use the zero feature under
Graph y =
the CALC menu to determine on what interval(s)
on [0, 2π). Use the
Graph y = cos x and y =
sin x − 1 < 0.
intersect feature under the CALC menu to
determine on what interval(s) cos x ≤
.
The zeros of
sin x − 1 are about 0.785 or
and
about 2.356 or
. The graph is below the x-axis
when 0 ≤ x <
or
< x < 2π.
Therefore,
sin x − 1 < 0 on 0 ≤ x <
or
<
The graphs intersect at about 2.618 or
and about
x < 2π.
3.665 or
. The graph of y = cos x is below the
56.
REFRACTION When light travels from one
≤ x ≤
other graph when
.
medium to another it bends or refracts, as shown.
Therefore, cos x ≤
≤ x ≤
on
.
55.
sin x − 1 < 0
SOLUTION:
Refraction is described by n
sinθ
= n
sinθ
, where
2
1
1
2
sin x − 1. Use the zero feature under
Graph y =
n
is the index of refraction of the medium the light
the CALC menu to determine on what interval(s)
1
sin x − 1 < 0.
is entering, n
is the index of refraction of the
2
medium the light is exiting, θ
is the angle of
1
incidence, and θ
is the angle of refraction.
2
a. Find θ
for each material shown if the angle of
2
incidence is 40º and the index of refraction for air is
1.00.
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