ฟั งก์ชนั ตรีโกณมิติ (Trigonometry Function) 1
สมการตรีโกณมิติ
1. ใ ้นักเรียน าคำตอบของ มการในแต่ละข้อต่อไปนี้ เมื่อ 0
x 2π
1 4sin 2 x − 3 = 0
…………………………………………………………………………………………………………………………………………………………………………………
-
I
+sinx" sinx sinx
………………………………………………………………………………………………………………………………………………………………………………… E
= =
3 =
sinx"
…………………………………………………………………………………………………………………………………………………………………………………
>
=
=
X
I
X =
…………………………………………………………………………………………………………………………………………………………………………………
= E
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
sinx
= ·: X
=
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
2. tan x sin x + tan x = 0
…………………………………………………………………………………………………………………………………………………………………………………
tanx (sinx + 1) 0
…………………………………………………………………………………………………………………………………………………………………………………
=
…………………………………………………………………………………………………………………………………………………………………………………
non tanx o no 2 sinx + 1 0
…………………………………………………………………………………………………………………………………………………………………………………
= =
X = 0 180 300 sinx -1
…………………………………………………………………………………………………………………………………………………………………………………
,
=
,
X 290
………………………………………………………………………………………………………………………………………………………………………………… =
fan 290
…………………………………………………………………………………………………………………………………………………………………………………
*
eastai a
…………………………………………………………………………………………………………………………………………………………………………………
i X 0 180 388
…………………………………………………………………………………………………………………………………………………………………………………
=
, ,
…………………………………………………………………………………………………………………………………………………………………………………
คณิตศาสตร์เพิ่มเติม 3 โรงเรียนเตรียมอุดมศึกษาพัฒนาการสุวรรณภูมิ
ฟั งก์ชนั ตรีโกณมิติ (Trigonometry Function) 2
3. 2cos 2 x − 3 cos x = 0
…………………………………………………………………………………………………………………………………………………………………………………
cosx(z(oSX (3) 0 =
…………………………………………………………………………………………………………………………………………………………………………………
-
…………………………………………………………………………………………………………………………………………………………………………………
Mimin 1 cosX 0 nirniz 20sX-53 0
…………………………………………………………………………………………………………………………………………………………………………………
= =
E
X COSX
…………………………………………………………………………………………………………………………………………………………………………………
90 27
=
,
:
…………………………………………………………………………………………………………………………………………………………………………………
30 90 240 338
…………………………………………………………………………………………………………………………………………………………………………………
i X =
, , ,
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
4. 4sin3 x − sin x = 0
Asinix-1 0 ② =
…………………………………………………………………………………………………………………………………………………………………………………
sinx 14sin2x-17 = g 4In X E
…………………………………………………………………………………………………………………………………………………………………………………
norie sinx 0
…………………………………………………………………………………………………………………………………………………………………………………
= =
2sinx =
1
…………………………………………………………………………………………………………………………………………………………………………………
sinx
=1
=
80 188 300
=
…………………………………………………………………………………………………………………………………………………………………………………
, ,
sinx sinx -
1
…………………………………………………………………………………………………………………………………………………………………………………
=
:
: 0 30 ; 150 ; 180 210 , 320 300
…………………………………………………………………………………………………………………………………………………………………………………
,
, ,
X = 38 138
210 335X =
,
,
…………………………………………………………………………………………………………………………………………………………………………………
5. 3 cosec 2 x + 2cosec x = 0
…………………………………………………………………………………………………………………………………………………………………………………
cose(x (coseX + 2)2y
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
Cose = j E3coSe) + 2 Ef
…………………………………………………………………………………………………………………………………………………………………………………
V3(0/2) 2
………………………………………………………………………………………………………………………………………………………………………………… = -
= an ma cosel
…………………………………………………………………………………………………………………………………………………………………………………
>
= -
3
…………………………………………………………………………………………………………………………………………………………………………………
248" 305 #
…………………………………………………………………………………………………………………………………………………………………………………
=
,
Mow 200 , 300 #
…………………………………………………………………………………………………………………………………………………………………………………
คณิตศาสตร์เพิ่มเติม 3 โรงเรียนเตรียมอุดมศึกษาพัฒนาการสุวรรณภูมิ
ฟั งก์ชนั ตรีโกณมิติ (Trigonometry Function) 3
6. ( tan x − 1) ( 4sin 2 x − 3) = 0
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
7. sin 2 x − cos x + 5 = 0 (Bison Granimiton) (sinix + cos* 1) =
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
8. 3sec x − cos x + 2 = 0
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
คณิตศาสตร์เพิ่มเติม 3 โรงเรียนเตรียมอุดมศึกษาพัฒนาการสุวรรณภูมิ
ฟั งก์ชนั ตรีโกณมิติ (Trigonometry Function) 4
x
9. cos 2x + 2cos 2
=1
2
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
10. 2sin 2 x − 3cos x − 3 = 0
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
11. cot x + 2sin x = cosec x
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
คณิตศาสตร์เพิ่มเติม 3 โรงเรียนเตรียมอุดมศึกษาพัฒนาการสุวรรณภูมิ
ฟั งก์ชนั ตรีโกณมิติ (Trigonometry Function) 5
12. 4tan 2 − 3sec2 = 0
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
13. cos 2 = sin
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
14. 2cos2 + 2cos2 = 1
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
คณิตศาสตร์เพิ่มเติม 3 โรงเรียนเตรียมอุดมศึกษาพัฒนาการสุวรรณภูมิ
ฟั งก์ชนั ตรีโกณมิติ (Trigonometry Function) 6
15. sec2 − 2tan = 0
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
5
16. cos θ + secθ =
2
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
17. 2 cos2 x + 3sin x − 3 = 0
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
คณิตศาสตร์เพิ่มเติม 3 โรงเรียนเตรียมอุดมศึกษาพัฒนาการสุวรรณภูมิ
ฟั งก์ชนั ตรีโกณมิติ (Trigonometry Function) 7
18. sec2 x + tan x − 1 = 0
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………………
คณิตศาสตร์เพิ่มเติม 3 โรงเรียนเตรียมอุดมศึกษาพัฒนาการสุวรรณภูมิ
