toán luyện tập 11 chương 1 lượng giác

Luyện tập 1 toán 11 – Hàm số lượng giác và phương trình lượng giác
Phần 1: tập xác định của hàm số:
 2π

+ 2x ÷
a) y = tan 
 3

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
π
b) y = cot  x − ÷
4

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2x
c) y = cos
x −3
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2 cos x
d) y =
3sin 2 x
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sin x + 1
1 − sin x
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2 + cot x
f) y =
cos2 x − sin 2 x
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e) y =

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1
g) y = 2 + sin x −
2
tan x − 1
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tan x
h) y =
sin x − cos x
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1− x
1+ x
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k) y = sin x + cos x
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i) y = sin

2 − cos x
tan x.cot x
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l) y =


Phần 2: Giá trị lớn nhất – Giá trị nhỏ nhất của hàm lượng giác

π
a) y = 3sin  x − ÷− 2
6

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2

b) y = 4sin x − cos2 x
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c) y = 3 cos2 x + 1
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d) y = 7 − 3 sin3 x
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Phần 3: Phương trình lượng giác cơ bản:
1
2
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a) sin3 x =


π

b) tan  x − ÷ = 3
4

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2
2
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c) cos2 x = −

d) sin3 x − sin 3 x.cos x = 0
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e) tan 4 x.cot 2 x = 1
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f) sin3 x − cos2 x = 0
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
π
g) tan  2 x + ÷+ tan 3 x = 0
3

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2

2
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h) cos4 x − sin 4 x =


π
i) 2 cos  x − ÷+ 1 = 0
6

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x
=0
2
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k) cos x − 2sin 2


2
8
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l) sin3 x cos x − cos3 x sin x =

m) cos2 x + cos2 2 x + cos2 3 x = 1
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.
 17π

2
2
+ 10 x ÷
n) sin 2 x − cos 8 x = sin 
 2

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o) cos4 x + sin 6 x = cos2 x
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1 − cos 4 x
sin 4 x
−
=0
2sin 2 x 1 + cos 4 x
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.
p)

2 +1
2
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q) sin x cos x + cos2 x =

x π
2 − 3 ) cos x − 2sin  − ÷
(
r)
2 4
2

=1
2 cos x − 1
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Phần 3: Các phương trình lượng giác đơn giản
1) Phương trình bậc hai đối với một hàm số lượng giác:
2
a) 4 cos x − 2

(

)

3 + 1 cos x + 3 = 0

b) 3cos2 x + 4sin x − 4 = 0
c) 2 cos2 x − 8cos x + 6 = 0
d) 2 cos x cos2 x = 1 + cos2 x + cos3 x
e)

3
= 3 + 2 tan 2 x
2
cos x

f) 6sin 2 3 x + cos12 x = 4
2
g) sin x +


1
1 
− 2  sin x +
÷= 1
2
sin x 
sin x


2) Phương trình bậc nhất theo sinx cosx (Phương trình cổ điển)
a)

3 cos x − sin x = 2

b) cos x + 3 sin x = −1
c) sin3 x + 3 cos3x = 2
d) cos6 x − sin 4 x = 3(cos 4 x − sin 6 x )
e)

3(1 − cos2 x )
= cos x
2sin x

f) 3sin 3 x − 3 cos9 x = 1 + 4sin 3 x
3) Phương trình thuần nhất bậc hai theo sinx và cosx:

(

)

2
2
a) 3sin x + 8sin x cos x + 8 3 − 9 cos x = 0

b) 4sin 2 x + 3sin 2 x − 2 cos2 x = 4


c) sin3 x + 2sin 2 x cos x − 3cos3 x = 0

d) 2 tan x + cot x = 3 +

2
sin 2 x

4) Phương trình đối xứng
a) 2(sin x + cos x ) + 3sin x cos x + 2 = 0
b) sin3 x + cos3 x = 1 − sin x cos x
c) cos x − sin x − 2sin 2 x − 1 = 0
d) sin x + cos x =

cos2 x
1 − sin 2 x