5-3 Solving Trigonometric Equations Worksheet With Answers Page 4
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28interval (–
, ), are found by adding integer
The equation cos x = 2 has no real solutions since
multiples of 2π. Therefore, the general form of the
the maximum value the cosine function can obtain is
1. On the interval [0, 2π), the equation
has
5-3 Solving Trigonometric Equations
solutions is
+ 2nπ,
+ 2nπ,
.
solutions 0 and π.
2
Find all solutions of each equation on [0, 2 ).
15.
4 cot x = cot x sin
x
4
2
13.
sin
x + 2 sin
x − 3 = 0
SOLUTION:
SOLUTION:
The equations sin x = 2 and sin x = –2 have no real
solutions. On the interval [0, 2π), the equation cot x =
On the interval [0, 2π),
when x =
and
0 has solutions
and
.
when x =
. Since
is not a real
2
16.
csc
x – csc x + 9 = 11
number, the equation
yields no
SOLUTION:
additional solutions.
14.
–2 sin x = –sin x cos x
SOLUTION:
On the interval [0, 2π), the equation csc x = –1 has a
solution of
and the equation csc x = 2 has
solutions of
and
.
The equation cos x = 2 has no real solutions since
the maximum value the cosine function can obtain is
3
2
17.
cos
x + cos
x – cos x = 1
1. On the interval [0, 2π), the equation
has
solutions 0 and π.
SOLUTION:
2
15.
4 cot x = cot x sin
x
SOLUTION:
On the interval [0, 2π), the equation cos x = 1 has a
solution of 0 and the equation cos x = –1 has a
The equations sin x = 2 and sin x = –2 have no real
solution of π.
solutions. On the interval [0, 2π), the equation cot x =
and
2
0 has solutions
.
18.
2 sin
x = sin x + 1
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Page 4
SOLUTION:
2
16.
csc
x – csc x + 9 = 11
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