5-3 Solving Trigonometric Equations Worksheet With Answers Page 2
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28are found by adding integer multiples of π.
interval (–
, ), are found by adding integer
multiples of 2π. Therefore, the general form of the
Therefore, the general form of the solutions is
+
5-3 Solving Trigonometric Equations
solutions is
+ 2nπ,
+ 2nπ,
.
nπ,
.
2
5.
7.
9 + cot
x = 12
3 csc x = 2 csc x +
SOLUTION:
SOLUTION:
The period of cosecant is 2π, so you only need to
find solutions on the interval
. The solutions
on this interval are
and
. Solutions on the
The period of cotangent is π, so you only need to find
solutions on the interval
. The solutions on this
interval (–
, ), are found by adding integer
multiples of 2π. Therefore, the general form of the
interval are
and
. Solutions on the interval (–
solutions is
+ 2nπ,
+ 2nπ,
.
, ), are found by adding integer multiples of π.
Therefore, the general form of the solutions is
+
2
8.
11 = 3 csc
x + 7
SOLUTION:
nπ,
+ nπ,
.
6.
2 – 10 sec x = 4 – 9 sec x
SOLUTION:
The period of secant is 2π, so you only need to find
solutions on the interval
. The solutions on
The period of cosecant is 2π, so you only need to
find solutions on the interval
. The solutions
this interval are
and
. Solutions on the
on this interval are
,
,
, and
. Solutions
interval (–
, ), are found by adding integer
multiples of 2π. Therefore, the general form of the
on the interval (–
, ), are found by adding integer
multiples of 2π. Therefore, the general form of the
solutions is
+ 2nπ,
+ 2nπ,
.
solutions is
+ 2nπ,
+ 2nπ,
+ 2nπ,
+
7.
3 csc x = 2 csc x +
2nπ,
.
SOLUTION:
2
9.
x – 2 = 4
6 tan
SOLUTION:
The period of cosecant is 2π, so you only need to
find solutions on the interval
. The solutions
on this interval are
and
. Solutions on the
interval (–
, ), are found by adding integer
multiples of 2π. Therefore, the general form of the
The period of tangent is π, so you only need to find
solutions is
+ 2nπ,
+ 2nπ,
.
solutions on the interval
. The solutions on this
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Page 2
interval are
and
. Solutions on the interval (–
2
8.
11 = 3 csc
x + 7
, ), are found by adding integer multiples of π.
SOLUTION:
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