5-3 Solving Trigonometric Equations Worksheet With Answers Page 20
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28medium 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
5-3 Solving Trigonometric Equations
incidence is 40º and the index of refraction for air is
1.00.
water:
b. If the angle of incidence is doubled to 80 , will
b. Find the angle of refraction for one of the
the resulting angles of refraction be twice as large as
mediums using an angle of incidence of 80 .
those found in part a ?
glass:
SOLUTION:
a. glass:
θ
≈ 25 when θ
= 40 andθ
≈ 40.4 when θ
=
2
1
2
1
80 . Therefore, the angle of refraction is not twice
as large.
ice:
57.
ERROR ANALYSIS Vijay and Alicia are solving
2
x – tan x +
=
tan x. Vijay thinks that
tan
the solutions are x =
+ n , x =
+ n , x =
+ n , and x =
+ n . Alicia thinks that the
solutions are x =
+ n
and x =
+ n . Is
either of them correct? Explain your reasoning.
plastic:
SOLUTION:
2
First, solve tan
x – tan x +
=
tan x.
water:
On [0, 2π) tan x = 1 when x =
and x =
and
tan x =
when x =
and x =
.
Sample answer: Therefore, Vijay’s solutions are
correct; however, they are not stated in the simplest
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Page 20
form. For example, his solutions of x =
+ n
and
b. Find the angle of refraction for one of the
mediums using an angle of incidence of 80 .
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