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(Hard) Trig Equations Worksheet Find all solutions to the following equations that fall in 0, 2π [ ) 1) 8 sin 3 x + 4 sin 2 x 6 sin x = 3 Hint: Factor by grouping 2) tan x 2 ( ) = 0 Hint: there are 4 solutions 3) cos 2 arcsin x ( ) = 13 11x Hint: Choose your 2x angle formula carefully.

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Transcript of (Hard)'Trig'Equations'Worksheet' Find'all'solutions'to'the...

(Hard)'Trig'Equations'Worksheet'

Find'all'solutions'to'the'following'equations'that'fall'in' 0, 2π[ ) ''!

1) 8sin3 x + 4sin2 x − 6sin x = 3 !!!

Hint:!Factor!by!grouping!

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2) tan x2( ) = 0 !Hint:!there!are!4!solutions!!

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3) cos 2arcsin x( ) = 13−11x !!Hint:!Choose!your!2x!angle!formula!carefully.!

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4) cos x + sin x2

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⎞⎠⎟ = 0 !!

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5) sin x + 2x( ) = 0 !!Hint:!Angle!addition!formula,!then!2x!angle!formula.!Easier!way?!

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sin A + B( ) = sinAcosB + cosAsinB !!sin A − B( ) = sinAcosB − cosAsinB !cos A + B( ) = cosAcosB − sinAsinB !cos A − B( ) = cosAcosB + sinAsinB !

tan A + B( ) = tanA + tanB1− tanA tanB

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tan A − B( ) = tanA − tanB1+ tanA tanB

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sin 2x( ) = 2sin xcos x !!cos 2x( ) = cos2 x − sin2 x !! = 1− 2sin2 x !

= 2cos2 x −1 !!

tan 2x( ) = 2 tan x1− tan2 x

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sin x2

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⎞⎠⎟ = ± 1− cos x

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cos x2

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⎞⎠⎟ = ± 1+ cos x

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tan x2

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⎞⎠⎟ =

1− cos xsin x

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= sin x1− cos x

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