Question

Materi : ID . 3GONOMET3
Kelas : XI SMA

Dijawab ya kak/om/bu' ....

Answer 1

Verified answer

23)
Diketahui:
*tetha nya gak ada di keyboard jadi pake simbol @ aja yaa.*
0° < @ < 90°

1 + sin [email protected] = 2 cos² [email protected]
sin [email protected] = 2 cos² [email protected] - 1
sin [email protected] = cos ([email protected][email protected])
*rumus cos sudut rangkap*
sin [email protected] = cos [email protected]

sin [email protected] = sin (90°[email protected])
[email protected] = (90° - [email protected]) ± k.360°
[email protected] = 90° ± k.360°
@ = 15° ± k.60°
@ = 15° dan @ = 75°

sin [email protected] = sin (90°[email protected])
sin [email protected] = sin (180°-(90°[email protected]))
[email protected] = (90° + [email protected]) ± k.360°
[email protected] = 90° ± k.360°
@ = -45° ± k.180°
*tidak memenuhi*


1 + sin [email protected] = 2 cos² [email protected]
1 + sin [email protected] - 2(1 - sin² [email protected]) = 0
2 sin² [email protected] + sin [email protected] - 1 = 0
(2 sin [email protected] - 1)(sin [email protected] + 1) = 0

sin [email protected] = 1/2
sin [email protected] = sin 30°
@ = 15°
dan
sin [email protected] = -1
sin [email protected] = sin 270°
@ = 135°
*tidak memenuhi*

Jadi @ yang memenuhi {15°, 75°} C



24)
180° < x < 270°

9 tan² x - 24 tan x + 16 = 0
(3 tan x - 4)² = 0
3 tan x = 4
tan x = 4/3

Karena x di Kuadran III maka
sin x =
sin x = -
Jawabannya D


25)

12 sin² x + sin x - 1 = 0
*menggunakan rumus abc*
sin x1 = 1/4
dan
sin x2 = -1/3

csc² x1 + csc² x2 - 7
= (4)² + (-3)² - 7
= 16 + 9 - 7
= 18
Jawabannya A