Therefore, on the interval [0, 2π) the solutions are
,
5-3 Solving Trigonometric Equations
Find all solutions of each equation on the
interval [0, 2 ).
, and
.
23. tan 2 x = 1 – sec x
SOLUTION: 21. 1 = cot 2 x + csc x
SOLUTION: Therefore, on the interval [0, 2π) the solutions are 0,
, and
Therefore, on the interval [0, 2π) the solutions are
,
, and
.
.
25. 2 – 2 cos2 x = sin x + 1
SOLUTION: 23. tan 2 x = 1 – sec x
SOLUTION: Check
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Therefore, on the interval [0, 2π) the solutions are 0,
Therefore, on the interval [0, 2π) the solutions are
5-3 Solving
Equations
, and Trigonometric
.
25. 2 – 2 cos2 x = sin x + 1
,
, and
.
27. 3 sin x = 3 – 3 cos x
SOLUTION: SOLUTION: Check
Therefore, on the interval [0, 2π) the only valid
solutions are
and 0.
29. sec2 x – 1 + tan x –
tan x =
SOLUTION: Therefore, on the interval [0, 2π) the solutions are
,
, and
.
27. 3 sin x = 3 – 3 cos x
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Therefore, on the interval [0, 2π) the only valid
Therefore, on the interval [0, 2π) the solutions are
5-3 solutions
SolvingareTrigonometric
Equations
and 0.
29. sec2 x – 1 + tan x –
tan x =
,
,
and
.
77. Which of the following is not a solution of 0 = sin
2
+ cos tan
SOLUTION: ?
A
B
C 2π
D
SOLUTION: Try choice A.
Try choice B.
Try choice C.
Therefore, on the interval [0, 2π) the solutions are
,
,
and
.
Try choice D.
77. Which of the following is not a solution of 0 = sin
2
+ cos tan
?
A
The correct answer is D.
B
C 2π
D
SOLUTION: Try choice A.
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