Solving Trigonometric Equations MATH 109 - Precalculus S. Rook.
Solving a Trigonometric Equation Find the general solution of the equation.
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Transcript of Solving a Trigonometric Equation Find the general solution of the equation.
![Page 1: Solving a Trigonometric Equation Find the general solution of the equation.](https://reader036.fdocuments.in/reader036/viewer/2022062305/5697c0251a28abf838cd5749/html5/thumbnails/1.jpg)
Solving a Trigonometric EquationFind the general solution of the equation.
1cos2 .1 2 x2 2
x2cos2
1
xcos2
2
2
2cos 1x
4
x
4
4
4
4
3,
4
x
2
n
4
4
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Solving a Trigonometric EquationFind the general solution of the equation.
29tan 7 .2 x
7 7xtan 1
1tan 1 x
4
3x
4
4
4
7,
4
3x n
4
7tan 7 x
42
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Solving a Trigonometric EquationFind the general solution of the equation.
21cot .3 2 xx2cot 3
xcot 3
3
3tan 1x
6
x
6
6
6
6
5,
6
x n
6
6
xtan3
3
6
5,
n
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Solving a Trigonometric EquationFind the general solution of the equation.
3 cos2 .4 x2 2
xcos2
3
2
3cos 1x
6
x
6
62
6
11,
6
x n2
6
6
11,
n2
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Solving a Trigonometric EquationFind the general solution of the equation.
01 cot .5 x
xtan 1 1tan 1 x
4
3x
4
4
4
7,
4
3x n
4
1cot x
42
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Solving a Trigonometric EquationFind the general solution of the equation.
034sin .6 2 xx2sin4 3
xsin2
3
2
3sin 1x
3
x
3
3
3
3
2,
3
x n
3
3
3
2,
n4 4
x2sin4
3
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Factoring to Solve a Trigonometric EquationSolve the equation in the interval 0 < x < 2.
0sinsin .7 2 xx 0 sin x xsin
0sin x 1sin x0x
1
,2
x
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Factoring to Solve a Trigonometric EquationSolve the equation in the interval 0 < x < 2.
xxx cossin2sin 3 .8
0 sin x 3
0sin x
3cos2 x
0x
xcos2
,6
x
0cossin2sin 3 xxx
2
3cos x
6
11,
6
62
6
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Factoring to Solve a Trigonometric EquationSolve the equation in the interval 0 < x < 2.
01sin1cos .9 xx
1cos x
0x2
x
1sin x
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Factoring to Solve a Trigonometric EquationSolve the equation in the interval 0 < x < 2.
xxx tan2sectan .10
0 tan x xsec
0tan x
2sec x
0x
2
,4
x
0tan2sectan xxx
2
2cos x
4
7,
4
42
4
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Factoring to Solve a Trigonometric EquationSolve the equation in the interval 0 < x < 2.
xxx sintansin .11
0 sin x xtan
0sin x
0x
1
,4
x
0sintansin xxx
1tan x
4
5,
4
4
4
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Factoring to Solve a Trigonometric EquationSolve the equation in the interval 0 < x < 2.
0tantan .12 2 xx 0 tan x 1
0tan x
0x
xtan
,4
3x
1tan x
4
7,
4
4
4
42
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Using the Quadratic FormulaSolve the equation in the interval 0 < x < .
03sinsin2 .13 2 xx 0 xsin2
3sin2 x 1sin x3
2
x
xsin 1
2
3sin x
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Using the Quadratic FormulaSolve the equation in the interval 0 < x < .
01tan3tan2 .14 2 xx
tan x 3 9 4 2 14
4
93tan
x 8
4
173
781.1281.0
781.1tan 1x06.1x
281.0tan 1 x
87.2x274.0
274.0
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Using the Quadratic FormulaSolve the equation in the interval 0 < x < .
2cos3cos5 .15 2 xx
cos x 3 9 4 5 2
10
10
93cos
x 40
10
493
4.01
4.0cos 1x16.1x
1cos 1 xx
02cos3cos5 2 xx
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Using the Quadratic FormulaSolve the equation in the interval 0 < x < .
2cos4cos .16 2 xx
cos x 4 16 4 1 2
2
2
614cos
x
82
84
414.3586.0
586.0cos 1x945.0x
02cos4cos2 xx
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