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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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-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____

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-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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-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 }