(Hard)'Trig'Equations'Worksheet' Find'all'solutions'to'the...
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(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
⎛⎝⎜
⎞⎠⎟ = 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 + 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
⎛⎝⎜
⎞⎠⎟ = ± 1− cos x
2!!
cos x2
⎛⎝⎜
⎞⎠⎟ = ± 1+ cos x
2!
tan x2
⎛⎝⎜
⎞⎠⎟ =
1− cos xsin x
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= sin x1− cos x
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