Trig Equations Worksheet Find all solutions to the following equations that fall in [ 0,
1) 2sin x cos x − 2 sin x = 0 2) tan x − 2sin x = 0 3) 6sin 2 x − 7sin x − 5 = 0 5
4) − sin 2 x + cos x = − 4
2π ) 5) 8sin 3 x + 4 sin 2 x − 6sin x = 3 Hint: Factor by grouping 6) cos ( 2x ) + sin x = 0 7) cos ( 2 arcsin x ) = 1− x 8) tan 6 x − 9 tan 2 x = 0 ⎛ x⎞
9) cos x + cos ⎜ ⎟ = 0 ⎝ 2⎠
Hint: Apply a half angle formula, ignore plus/minus, instead check answers at the end 10) sin ( x + 2x ) = 0 Hint: Angle addition formula, then 2x angle formula. Easier way? ____________________________________________________________________________________________ sin ( A + B ) = sin A cos B + cos Asin B 2 tan x
sin ( A − B ) = sin A cos B − cos Asin B tan ( 2x ) =
2
1−
tan
x
cos ( A + B ) = cos A cos B − sin Asin B 1− cos x
⎛ x⎞
cos ( A − B ) = cos A cos B + sin Asin B sin ⎜ ⎟ = ±
⎝ 2⎠
2
tan A + tan B
tan ( A + B ) =
1+ cos x
⎛ x⎞
1− tan A tan B
cos ⎜ ⎟ = ±
⎝ 2⎠
2
tan A − tan B
tan ( A − B ) =
⎛ x ⎞ 1− cos x
1+ tan A tan B
tan ⎜ ⎟ =
⎝ 2⎠
sin x
sin ( 2x ) = 2sin x cos x sin x
=
2
2
cos ( 2x ) = cos x − sin x 1− cos x
= 1− 2sin 2 x 2
= 2 cos x − 1