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Worksheet by Kuta Software LLC
Precalculus
Solving Trig Equations Notes
Name___________________________________
Date________________ Period____
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-1-
Find all solutions to each equation in radians.
1) -3 2 = 6cos q2) -2 + tan q =
-6 - 3
3
3) -2 3 = -2cos q
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Worksheet by Kuta Software LLC
-2-
4) -1 + sin -4q = -2 - 3
25) -4 + tan
q
3 = -5
6) -1 + sin (q + 11p
6 ) = -2 + 2
2
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Worksheet by Kuta Software LLC
-3-
Solve each equation for 00 £ £ qq < < 22pp .
7) 4 = sin2 q + 3 8) 3cos2 q = -1 + 4cos2 q
9) 2cos q sin q = -cos q
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Worksheet by Kuta Software LLC
-4-
10) sin q tan q - 3sin q = 0 11) -4sin2 q = 1 - 3sin q - 2sin2 q
12) 4cos q - 4cos2 q = 1
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Worksheet by Kuta Software LLC
Precalculus
Solving Trig Equations Notes
Name___________________________________
Date________________ Period____
©y g2y0j1a8d BKruetva` gSEo[fDt\w_acrFeW ELrLvCo.\ R dAvltlB prTiCgzh[tIsb IrCeZspeFrQvMeGdA.
-1-
Find all solutions to each equation in radians.
1) -3 2 = 6cos q
{3p
4 + 2pn,
5p
4 + 2pn}
2) -2 + tan q = -6 - 3
3
{11p
6 + pn}
3) -2 3 = -2cos q
No solution.
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Worksheet by Kuta Software LLC
-2-
4) -1 + sin -4q = -2 - 3
2
{- 5p
12 -
pn2
, -p
3 -
pn2 }
5) -4 + tanq
3 = -5
{21p
4 + 3pn}
6) -1 + sin (q + 11p
6 ) = -2 + 2
2
{- 19p
12 + 2pn, -
13p
12 + 2pn}
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Worksheet by Kuta Software LLC
-3-
Solve each equation for 00 £ £ qq < < 22pp .
7) 4 = sin2 q + 3
{p
2,
3p
2 }8) 3cos2 q = -1 + 4cos2 q
{0, p}
9) 2cos q sin q = -cos q
{p
2,
7p
6,
3p
2,
11p
6 }
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Worksheet by Kuta Software LLC
-4-
10) sin q tan q - 3sin q = 0
{0, p
3, p,
4p
3 }11) -4sin2 q = 1 - 3sin q - 2sin2 q
{p
6,
p
2,
5p
6 }
12) 4cos q - 4cos2 q = 1
{p
3,
5p
3 }
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