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### Transcript of (Hard)'Trig'Equations'Worksheet' Find'all'solutions'to'the ... stonelakb/math/pdf/Trig...

• (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 x 2

⎛ ⎝⎜

⎞ ⎠⎟ = 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 + tanB

1− tanA tanB !!

tan A − B( ) = tanA − tanB 1+ 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 x 1− tan2 x

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sin x 2

⎛ ⎝⎜

⎞ ⎠⎟ = ±

1− cos x 2

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cos x 2

⎛ ⎝⎜

⎞ ⎠⎟ = ±

1+ cos x 2

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tan x 2

⎛ ⎝⎜

⎞ ⎠⎟ =

1− cos x sin x

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= sin x 1− cos x

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