disequazioni goniometriche

Esercizi di trigonometria semi-svolti

!

1

2 sin x

' ( )

2 cos x

*

+

"

sin x

' ( ) *

&

%

2

$

$ #

2 cos2 x

0

sin x

cos2 x

3

4cos x sin x

Per ciascuna delle seguenti disequazioni individua nel piano CS le relative zone valide e le relative soluzioni per l’incognita x

2

1.5 1.5 1 1 0.5 -1.5

-1

0.5

-0.5

0.5

1

1.5

-1.5 -1 -0.5

0.5

-0.5

-0.5

-1

-1

1

1.5

-1.5

sin x

1

2cos2 x

1.5

2sin2 x

1 L

H I K

3cos x

2sin2 x

H I

0

H JI

<

2

H JI

8

2 sin x

: ;

8

: 7;

9

2

<

6

=

: ; <

: ; <

3 cos x

F G

> ? @ A DB C EC

5

4

9

8

2 cos x

7

2

8

7 6

, . / 20 1 31

-1.5

0

1.5 1

1 0.5

0.5 -1.5

-1

-0.5

0.5

1

1.5

-1.5

-1

-0.5

0.5

-0.5

-0.5 -1

-1 -1.5

-1.5

1

1.5

0

0

2 cos2 x

sin x

1

2cos x sin x

0

3 cos2 x

2

csc x sec x sin x 1.5

1.5

1

1

0.5 0.5 -1.5 -1 -0.5

0.5

1

1.5 -1.5

-0.5

-1

-0.5

0.5

1

1.5

-0.5

-1

-1

-1.5

1.5

0.5

1

;

3

0.5 0.5

-0.5

2 @

1

3 sin x

= > ?

= :>

cos x

;

1.5

-1.5 -1 -0.5

;

2 sin x

= :>

= :>

2 cos x

;

8

7 <

2

;

/ 0 1 2 53 4 64

0

:

+ .

+ --

,

+

1 cos x tan x

: 9

*

)

! " # $ '% & (&

-1.5

1

1.5 -1.5 -1 -0.5

0.5

-1

-0.5

-1.5

-1 -1.5

1

1.5

0

-1.5 -1 -0.5

4

/ 10

sin x

0

2cos x sin x / 0

/ 0 2

1

1.5

1

1.5

0

cos x

/ 0

/ 0 2

1.5

1.5

1 1 0.5 0.5 -1.5 -1 -0.5 -1.5

-1

-0.5

0.5

-0.5 -1 -1.5

1

1.5

0.5

-0.5 -1 -1.5

2 0 #

2

5

-1.5

,

-1.5

$ % & ' *( ) +)

-1

.

-1

,

-0.5

x

0.5

/ 0 6

1.5

-0.5

1

!

0.5 1

"

!

0.5

$ % & ' *( ) +) 3

3

1

0.5

2 cos x

2

1

sin2 x

sin2

2

1.5

cos2 x 2

2 sin x

0

1.5

-1.5 -1 -0.5

/ 10

2

2 cos x

2sin2 x

1

4sin x

4cos2 x