MHF 4U1
Trigonometric Equations
1. Solve for x, Ox2,r.
a) sinx=—-2
b) cosx=—
2
c) tanx=—1
d) secx
e) sinx
2x =
0 cos
=
—2
=
—
—
2. Solveforx,—2rxO.
a) cosx
b) tan
x
2
=
d) sin2x=
=
tanx
c) sin
2 x—sinx
=
2
2 =9
f) (2cscx—l)
x—3=O
2
e) 4cos
3. Solveforx,Ox22T.
a)
cos(2x) + cos x + 1
b) cos(2x) = sin x
c) 3 tan x = tan(2x)
g) sin(2x)+ cos(2x)= 0
e) sin(2x)cosx + sin
2x=1
h) 3cos(2x)+ 2 + cosx = 0
sin(2x)+ sinx = 0
i) sin(2x)= tanx
j)
k) 3sin(2x)+cosx = 0
1) 3sinx+cos(2x)= 2
=
0
d) sinx = 6sin(2x)
2 x—sin
cos
2x
=
2sinxcosx
4. Solve for x in the given interval.
a)
sinx—sinxtanx=O, Oxr
b) cosxtan(3x)=0, —rx0
c) ósin
x—5cosx—2=0, x
2
2
2
e) 2
x—3sin
cos
x
=1, —2nx2n
d) sinx+tanx=O, —x
0
2tanx=secx, —2rx0
5. Solve for x in the given interval.
a)
b) sin(2x)=cosx, Z x
cos(2x)=cos
x
2
, —r x ,r
c) cos
2x
—
2sinxcosx
—
2x
sin
=
0, 0
x
d) 2(sin x + cos
4 x)= 1,
—
,r
x
r
6. Solve for x in the given interval.
a)
cosx=, —2x2
b) sin(2x)=
c) 2
sin
x
+sinx=O, x
d) 2sin
x+sinx—1=0, 0x4
2
e) 2sec
x+3secx—2=0, 0x2
2
0
tanx+sec(2x)=1, x
x
-
—
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