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

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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 !!

    Hint:!Apply!a!half!angle!formula,!ignore!plus/minus,!instead!check!answers!at!the!end!

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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

    !!

    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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