5-3 Solving Trigonometric Equations Worksheet With Answers Page 22
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28the solutions are 0,
,
,
,
,
,
,
,
Therefore, after checking for extraneous solutions,
, and
.
5-3 Solving Trigonometric Equations
the solutions are
,
,
,
,
, and
.
2
2
2
2
59.
60.
REASONING Are the solutions of csc x =
4 cos
x – 4 sin
x cos
x + 3 sin
x = 3
and
2
cot
x + 1 = 2 equivalent? If so, verify your answer
SOLUTION:
algebraically. If not, explain your reasoning.
SOLUTION:
On [0, 2 ) sin x = 1 when x =
, sin x = –1 when
x =
, sin x = –
when x =
and x =
,
and sin x =
when x =
and x =
.
Therefore, after checking for extraneous solutions,
the solutions are
,
,
,
,
, and
.
The solutions to csc x =
are
and
. Using
60.
REASONING Are the solutions of csc x =
and
2
2
a Pythagorean identity, cot
x + 1 = 2 simplifies to
cot
x + 1 = 2 equivalent? If so, verify your answer
2
algebraically. If not, explain your reasoning.
csc
x = 2 or csc x = ±
. Therefore, there are
SOLUTION:
two additional solutions when csc x = –
and
:
2
. So, the solutions of csc x =
and cot
x + 1
= 2 are not equivalent.
OPEN ENDED Write a trigonometric equation
that has each of the following solutions.
61.
SOLUTION:
Sample answer: When sin x = 0, x = 0 and x = π.
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The solutions to csc x =
are
and
. Using
Page 22
When sin x =
, x =
and x =
. So, one
2
a Pythagorean identity, cot
x + 1 = 2 simplifies to
equation that has solutions of 0, π,
, and
is
2
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