重难点10三角函数中ω的范围与最值问题七大题型（原卷版）_11.4-2_2026-11-04

      
      
重难点10 三角函数中ω 的范围与最值问题【七大题型】

 1   !
"#$%&"'"()*+, ............................................................................2
 2   !
"-.%&"'"()*+, ............................................................................2
 3   !
"*+&"'"()*+, ................................................................................3
 4   !
"/0&"'"()*+, ................................................................................4
 5   !
"12&"'"()*+, ................................................................................4
 6   !
"3+&"'"()*+, ................................................................................5
 7  '"()*+,
%4"56, ............................................................................................5
17 !
8 ω "()*+,
 !
"9:%4;"<=>?@A !
"9:%48@ω "BC;DEF"G
H<27I2>?@JK=LM7NO"PQRS@TUVBWXY@Z["\]2^@_`;
abXc8"d2@eAXc8=fghi@jkBC.
\]2 1   !
8& ω "()*+,"l
1m !
8 ω "()*+"BCGn=oV%4@pl,K=&LqEHl
(1) !
"#$% ω "rs
(2) !
"-.% ω "rs
(3) !
"*+ ω "rs
(4) !
"/0% ω "rs
(5) !
"12 ω "rs
(6) !
"3+ ω "r.
\]2 2   !
8 ω "()*+,"Ctu
1mo !
"#$%B ω "Cvw
-xy\!
"#$z{"|G}~€
 ω "()",@‚ƒ@„y\"#$z{…†!
"#$z{"‡ˆ@V‰@=€y\!
"#$z{@Š‹oŒb{"rŽBC@@‘;
M@o’+“”•–WBC—†˜™.
2mo !
"-.%B ω "Ctu
 !
š›œ-.žŸšHœ-.8 {"“¢£{¤”†
@œ"-.ž¦-.8 
      
      
{"“¢£{¤”†
@§¨©„@abŽª« !
"-.%`¬­V/0%@C®,"¯Ax
°±²³´"vµ@¶·x ω "¸¹Qº@»‹ŽL¬­“ω”"¼+().
3mo !
"*+B ω "Ctu
‘y\ !
"*+@½o !
"*+-.žŸ/0"r@ŽL¾¿x ω "¸¹Q
(º)@»‹B¿ ω "+Ÿ¼+().
4mo !
"/0%B ω "Ctu
‘y\ !
"/0%@½o !
"/0-.ž7*+"r@¾¿x ω "¸¹Q(º)@
»‹B¿ ω "+Ÿ¼+().
 1   !
"#$%&"'"()*+,
À 1Á2024·<·ÃÄő!
𝑓(𝑥) = sin(2𝑥−𝜑)(0 ≤𝜑< π)A 0, π
3 Æ#$ÇÈ@½𝜑"*É+†Á    Å
Am
π
12
Bm
π
6
Cm
π
4
Dm
π
3
ÊQ 1-1Á2024·ËÌÍηGÄÅy\!
𝑦= sin(𝜔𝑥+ 𝜑)(𝜔> 0,𝜑∈(0,2π))"G›-.ž†𝑥= −
π
6@
Ï𝑓(𝑥)A π, 4π
3 Æ#$@½𝜔"*Ð+†Á    Å
Am
5
3
Bm2
Cm
8
3
Dm
10
3
ÊQ 1-2Á2024·ÑÒ·ÄÓÔÕÅy\!
𝑓(𝑥) = sin(𝜔𝑥+ 𝜑)(𝜔> 0)@‘Ö×𝑥=
π
4†!
𝑓(𝑥)9:"
G›-.ž@ 5π
3 ,0 †!
𝑓(𝑥)9:"GH-.8 @Ï𝑓(𝑥)A π
4 , 5π
6 Æ#$ÇØ@½𝜔"*Ð+†Á    Å
Am
9
17
Bm
18
17
Cm
12
17
Dm
24
17
ÊQ 1-3Á2024·ÙÚÛÜ·GÄÅy\!
𝑓(𝑥) = sin 𝜔𝑥+ 2π
3 (𝜔> 0)Az{
π
12 , π
6 Æ#$ÇÈ@½𝜔"
¼+();Á    Å
Am[2,5]
Bm[1,14]
Cm[9,10]
Dm[10,11]
 2   !
"-.%&"'"()*+,
À 2Á2023·ÙÝ·ÄÓÔÕő!
𝑓(𝑥) = 2sin(𝜔𝑥+ 𝜑)Á𝜔> 0@|𝜑| <
π
2ÅÞß𝑓(2𝑥) = 𝑓π
3 −2𝑥@Ï
𝑓(0) = −1@½𝜔"*É+†Á    Å
Am1
Bm2
Cm3
Dm4
ÊQ 2-1Á2024·>àáâ¦ã’·GÄÅy\!
𝑓(𝑥) = sin 𝜔𝑥−π
3 (𝜔> 0)Az{[0,π]Æ&Ïä&š›
      
      
-.ž@½𝜔"¼+();Á    Å
Am 11
6 , 17
6
Bm 17
6 , 23
6
Cm 11
6 , 17
6
Dm 17
6 , 23
6
ÊQ 2-2Á2023·åæзGÄÅ!
𝑓(𝑥) = sin(𝜔𝑥+ 𝜑)(𝜔> 0,0 < 𝜑< π)@‘¸¹Q𝑓(𝑥) ≤|𝑓
π
4𝜔|-
∀𝑥∈𝑅çè·@Ï𝑓(𝑥)"9éx𝑥=
π
8-.@½𝜔"*É+†Á    Å
Am1
Bm2
Cm3
Dm4
ÊQ 2-3Á2024·ÑÒ·ÄÓÔÕÅy\!
𝑓(𝑥) = sin(𝜔𝑥+ 𝜑)(𝜔> 0);Az{
π
18 , 5π
36 Æ"#$Ø!
@
V9:xÖ×𝑥= −
π
36-.@Ï fÁxÅ"GH12;𝑥=
7
72π@½𝜔"*É+†Á    Å
Am2
Bm12
Cm4
Dm8
 3   !
"*+&"'"()*+,
À 3Á2023·êëìηGÄÅy\!
𝑓(𝑥) = 2sin 𝜔𝑥−𝜋
6 (𝜔> 0)A 0, π
3 ÆíA*+@ÏA 2π
3 ,π Æ#
$@½𝜔"¼+();Á    Å
Am 0, 2
3
Bm 1, 5
3
Cm 5
2 , 8
3
Dm 11
4 , 17
3
ÊQ 3-1Á2024·îÜïηGÄő!
𝑓(𝑥) = 2sin 𝜔𝑥−π
3 ,(𝜔> 0)@𝑥∈0, π
2 "+ð†[−3,2]@½𝜔
"¼+();Á    Å
Am 5
3 ,4
Bm 5
6 , 10
3
Cm 5
6 , 5
3
Dm 5
3 , 10
3
ÊQ 3-2Á2024·êëñò·ÄÓÔÕÅy\!
𝑓(𝑥) = 4cos 𝜔𝑥−𝜋
12 (𝜔> 0),𝑓(𝑥)Az{ 0, 𝜋
3 Æ"*É+
ó†−𝜔@½ô&Þߛõ"𝜔"ö÷xz{Á    Å
Am(1,4]
Bm[4,7]
Cm(7,13)
Dm[13, + ∞)
ÊQ 3-3Á2023·øùúûü·GÄÅy\!
𝑓(𝑥) = 2sin(𝜔𝑥+ 𝜑)Á𝜔> 0@0 < 𝜑<
π
2Å"9:ý2
(0,1)@ÏAz{(π,2π)>¸íA*+@½𝜔"¼+();Á    Å
Am 0, 1
6
Bm 1
4 , 7
12
Cm 0, 1
6 ∪1
4 , 7
12
Dm 0, 1
6 ∪1
3 , 2
3
      
      
 4   !
"/0&"'"()*+,
À 4Á2023·êëñò·ÄÓÔÕÅþ!
𝑓(𝑥) = cos(𝜔𝑥+ 𝜑)(𝜔> 0,0 < 𝜑< π)"*Éÿ/0†𝑇@‘𝑓(𝑇)
=
3
2 @𝑥=
𝜋
9†𝑓(𝑥)"GH12@½𝜔"*É+†Á    Å
Am
3
2
Bm3
Cm6
Dm
15
2
ÊQ 4-1Á2024·ÑÒ·ÄÓÔÕÅy\!
𝑓(𝑥) = sin(2𝜋𝜔𝑥)(𝜔> 0)Az{(0,2)Æ#$@ÏAz{[0,18]
Æ& 5 H12@½𝜔"¼+()†Á    Å
Am 1
9 , 5
36
Bm 1
9 , 5
36
Cm 1
9 , 1
8
Dm 1
9 , 1
8
ÊQ 4-2Á2024·ÑÒ·ÄÓÔÕÅþ!
𝑓(𝑥) = cos(𝜔𝑥+ 𝜑)(𝜔> 0,0 < 𝜑< π)"*Éÿ/0†𝑇@‘𝑓(𝑇)
= −
1
2@Ï𝑥=
π
2†𝑓(𝑥)"G›-.ž@½𝜔"*É+†Á    Å
Am
2
3
Bm
4
3
Cm
8
3
Dm
10
3
ÊQ 4-3Á23-24 Ãq·ÜĀæā·0ĂÅy\!
𝑓(𝑥) = sin(𝜔𝑥+ 𝜑) 𝜔> 0,|𝜑|< π
2 "*Éÿ/0†
𝑇,𝑓𝑇
6 = 𝑓𝑇
3 @‘𝑓(𝑥)Az{[0,2]Æó& 8 H12@½𝜔"¼+();Á    Å
Am 7π
2 ,4π
Bm 4π, 9π
2
Cm 4π, 9π
2
Dm 7π
2 , 9π
2
 5   !
"12&"'"()*+,
À 5Á2023·ÑÒ·GÄÅy\!
𝑓(𝑥) = sin 𝜔𝑥+ π
3 (𝜔> 0)Az{ π
3 ,π Æó& 3 H12@½𝜔"¼+(
);Á    Å
Am 8
3 , 11
3 ∪4, 14
3
Bm 11
3 ,4 ∪
14
3 , 17
3
Cm[
11
3 ,
14
3 ) ∪(5,
17
3 )
Dm 14
3 ,5 ∪
17
3 , 20
3
ÊQ 5-1Á2023·ăĄąĆ·GÄÅć!
𝑓(𝑥) = cos 𝑥+ 2π
3 9:Æô&2"ĈĉĊʆċ`"
1
𝜔(𝜔> 0)@
ČĉĊ¸Ê@ôč9:Az{ 0, 2π
3 Æó&šH12@ÏA −π
12 , π
12 Æ#$ÇØ@½𝜔"¼+()†Á    Å
Am 9
4 ,3
Bm 9
4 ,4
Cm 11
4 ,4
Dm 11
4 ,6
ÊQ 5-2Á2024·ÑÒ·ÄÓÔÕÅy\!
𝑓(𝑥) = sin 𝜔𝑥+ π
3 (𝜔> 0)Az{ π
2 ,π ÆĎď&šH12@
½Đ
𝜔"¼+();Á    Å
      
      
Am 8
3 , + ∞
Bm 8
3 , + ∞
Cm 8
3 , 10
3
∪
11
3 , + ∞Dm 8
3 , 10
3 ∪11
3 , + ∞
ÊQ 5-3Á2024·êëđĒ·GÄÅy\!
𝑓(𝑥) = 2cos(𝜔𝑥+ 𝜑)Á𝜔> 0Ï−
π
2 < 𝜑<
π
2Å@ē T †!
𝑓(𝑥)
"*Éÿ/0@𝑓𝑇
4 = −1@‘𝑓(𝑥)Az{[0,1]&ÏĔ&H12@½𝜔"¼+();Á    Å
Am 17π
6 , 23π
6
Bm 17π
6 , 23
6 π
Cm 7π
3 , 10π
3
Dm 7π
3 , 10π
3
 6   !
"3+&"'"()*+,
À 6Á2023·êëèĕ·ÃÄÅć!
𝑓(𝑥) = sin 1
2 𝜔𝑥−π
6 (𝜔> 0)"9:Æô&2"ĈĉĊĖėĘċ`"
1
4@ČĉĊ¸Ê@čĘ!
𝑔(𝑥)"9:m‘𝑔(𝑥)A 0, π
3 Æ&Ïä& 3 H3+2@½𝜔"¼+()†Á    Å
Am 5
2 , 11
2
Bm 5
2 ,4
Cm 4, 11
2
Dm 11
2 ,7
ÊQ 6-1Á2023·ęæĚě·ÄÓÔÕÅy\ć!
𝑓(𝑥) = 2sin
𝜔𝑥
2 cos 𝜔𝑥
2 −3sin 𝜔𝑥
2 (𝜔> 0)"9:Ĝĝ£
Ğ
π
2𝜔H#ğąĠ@čĘ!
𝑔(𝑥)"9:@‘𝑔(𝑥)A(0,π)Æ& 3 H3+2@½𝜔"¼+()†Á    Å
Am 5
3 , + ∞
Bm 8
3 ,4
Cm 8
3 , 11
3
Dm 7
3 , 10
3
ÊQ 6-2Á2024·ġÝĢæ·GÄÅy\!
𝑓(𝑥) = sin 𝜔𝑥+ π
4 (𝜔> 0)Az{[0,π]Æ&Ïä& 4 H3+2@
ģ¿q¾êHĤĥ
①𝑓(𝑥)Az{(0,π)Æ&Ïä& 3 H¸Ħ"12s②𝑓(𝑥)"*Éÿ/0Žħ;
π
2s
③𝜔"¼+(); 13
4 , 17
4 s④𝑓(𝑥)Az{
π
23 , π
19 Æ#$ÇÈ.
V8ÿĤĥ"H
†Á    Å
Am1
Bm2
Cm3
Dm4
ÊQ 6-3Á2024·ÑÒ·ÄÓÔÕÅć!
𝑓(𝑥) = sin𝑥"9éĜĨ£Ğ
5π
6 H#ğąĠĩčĘ!
𝑔(𝑥)"9
é@Īć𝑔(𝑥)"9éÆī2"ČĉĊ¸Ê7ĈĉĊʆċ`"
1
𝜔Á𝜔> 0ÅĬ@čĘ!
ℎ(𝑥)"9é@Ïℎ(𝑥)
Az{(0,π)Æó&šH3+27šH12@½𝜔"¼+()†Á    Å
Am 7
6 , 8
3
Bm 5
3 , 13
6
Cm 5
3 , 13
6
Dm 7
6 , 8
3
 7  '"()*+,
%4"56,
À 7Á2024·ËÌĭĮ·ÄÓÔÕő!
𝑓(𝑥) = 3cos(𝜔𝑥+ 𝜑) 𝜔< 0，−π
2 < 𝜑< π
2 "*Éÿ/0†π@
      
      
Az{ −π
6 , π
6 Æ#$ÇØ@ÏAz{ 0, π
6 ÆíA12@½𝜑"¼+();Á    Å
Am π
6 , π
2
Bm −π
2 ,−π
3
Cm π
3 , π
2
Dm 0, π
3
ÊQ 7-1Á2024·ÑÒ·ÄÓÔÕÅy\!
𝑓(𝑥) = sin(2𝜔𝑥−𝜑)(𝜔> 0)Þß-įİ"𝑥∈R@ı&𝑓(𝑥) ≥𝑓
π
3 ,𝑓4π
3 + 𝑥= −𝑓4π
3 −𝑥@Ï𝑓(𝑥)A π
3 , 5π
6 Æ#$@½𝜔"*Ð+†Á   Å
Am
1
4
Bm
1
2
Cm
3
4
Dm
4
5
ÊQ 7-2Á2024·IJij·ÄÓÔÕÅy\𝑓(𝑥) = sin 𝜔𝑥+ π
3 + 𝜑
𝜔> 0,|𝜑|< π
2 †Ĵ!
@𝑔(𝑥) = sin
(𝜔𝑥+ 𝜑)@½q¾ĤĥĵĶ"H
†Á    Å
①𝜑=
π
6s
②‘𝑔(𝑥)"*Éÿ/0†3π@½𝜔=
2
3s
③‘𝑔(𝑥)Az{(0,π)Æ&Ïä& 3 H*+2@½𝜔"¼+()† 7
3 , 10
3 s
④‘𝑔π
4 =
3
2 @½𝜔"*É+† 2m
Am1 H
Bm2 H
Cm3 H
Dm4 H
ÊQ 7-3Á2023·ęæ·ÄÓÔÕÅy\!
𝑓(𝑥) = sin(𝜔𝑥+ 𝜑) 𝜔> 0,0 < 𝜑< π
2 ,𝑦= 𝑓𝑥+ π
4 ;Ĵ!
@
Ï𝑓−π
4 −𝑥+𝑓−π
4 + 𝑥= 0,𝑓(𝑥)A
π
18 , π
4 Æ#$@½𝜔"*Ð+†Á    Å
Am1
Bm3
Cm5
Dm
36
7
G7#
1mÁ2024·êëèĕ·ÄÓÔÕő!
𝑓(𝑥) = sin(𝜔𝑥)(𝜔> 0)A 0, π
4 Æ#$ÇÈ@½𝜔"¼+()†Á    Å
Am 0, 1
2
Bm(0,2)
Cm 0, 1
2
Dm(0,2]
2mÁ2024·<ÂĚηÄÓÔÕÅy\!
𝑓(𝑥) = 2sin𝜔𝑥(𝜔> 0)@½“
3
2 < 𝜔< 3”;“𝑓(𝑥)"9:Az{ −π
6 , π
3
ÆĔ&GH3+2”"Á    Å
Amķ~›õ
Bmĸ=›õ
Cmķ=›õ
DmĹķ~Ĺĸ=›õ
3mÁ2024·ËÌĭĮ·ÄÓÔÕÅē𝜔> 0@y\!
𝑓(𝑥) = sin 3𝜔𝑥−π
4 sin 2𝜔𝑥+ 5π
6 A(0,π)Æó& 6 H1
      
      
2@½𝜔¼+()†Á   Å
Am 19
12 , 7
4
Bm 17
12 , 19
12
Cm 13
12 , 17
12
Dm 3
4 , 13
12
4mÁ2024·ęÌ·ÄÓÔÕÅy\!
𝑓(𝑥) = sin(𝜔𝑥+ 𝜑) (𝜔> 0)@‘𝑓(0) =
2
2 @𝑓−π
3 = −𝑓5
6 π @½𝜔"
*É+†Á    Å
Am3
Bm1
Cm
6
7
Dm
2
3
5mÁ2024·êë·ÄÓÔÕÅy\!
𝑓(𝑥) = sin 𝜔𝑥+ π
3 Á𝜔> 0ÅAz{ 0, 5π
6 ÆĔ& 1 H12@Ïĺ𝑥∈
−2π
3 , π
6 Ļ@𝑓(𝑥)#$ÇÈ@½𝜔"¼+();Á    Å
Am 4
5 ,2
Bm 4
5 , 5
4
Cm 4
5 ,1
Dm 5
4 ,2
6mÁ2024·êë>Ü·ÄÅē!
𝑓(𝑥) = 2sin 𝜔𝑥+ π
3 (𝜔> 0)@‘íA𝑥1,𝑥2 ∈−π
6 , π
6𝜔@Ï𝑥1 ≠𝑥2@ļč
𝑓(𝑥1) = 𝑓(𝑥2) =
3@½𝜔"¼+();Á    Å
Am(0,12]
Bm[10, + ∞)
Cm[10,12]
Dm(6,10]
7mÁ2024·ęææò·ÄÓÔÕő!
𝑓(𝑥) = cos(𝜔𝑥+ 𝜑) 𝜔> 0,|𝜑|≤π
2 "9:x2 π
3 ,0 8 -.@Ï
𝑥= −
π
3;𝑓(𝑥)"3+2@𝑓(𝑥)Az{ 0, 2π
5 >&ĽG"3Ð+2@½𝜔"*Ð+†Á    Å
Am8
Bm7
Cm
27
4
Dm
25
4
8mÁ2024·ġÝĒľ·ÄÓÔÕÅy\!
𝑓(𝑥) = cos 𝜔𝑥+ π
4 (𝜔> 0)Az{ π
3 ,π Æ#$ÇØ@Ï𝑓(𝑥)Az
{(0,π)ÆĔ& 1 H12@½𝜔"¼+();Á    Å
Am 0, 1
4
Bm 1
2 , 3
4
Cm 1
4 , 3
4
Dm 1
4 , 5
4
Ã7^
9mÁ2024·îÜ·ÄÓÔÕÅy\!
𝑓(𝑥) = cos 𝜔𝑥+ π
3 (𝜔> 0)@½Á    Å
Amĺ𝜔= 2Ļ@𝑓𝑥−π
6 "9:x𝑥=
π
2-.
Bmĺ𝜔= 2Ļ@𝑓(𝑥)A 0, π
2 Æ"*Ð+† 3
2
Cmĺ𝑥=
π
6†𝑓(𝑥)"GH12Ļ@𝜔"*É+† 1
Dmĺ𝑓(𝑥)A −π
3 , π
6 Æ#$ÇØĻ@𝜔"*Ð+† 1
      
      
10mÁ2024·îÜïηÄÅy\!
𝑓(𝑥) = sin(𝜔𝑥+ 𝜑)(𝜔> 0),𝑥∈π
2 ,π "+ð;[𝑎,𝑏]@½q¾Ŀÿ
";Á    Å
Am‘𝑏−𝑎= 2,𝜑=
π
6@½𝜔¸íA*Ð+ Bm‘𝑏−𝑎= 2,𝜑=
π
6@½𝜔"*É+;
7
3
Cm‘𝑏−𝑎=
3@½𝜔"*É+;
4
3
Dm‘𝑏−𝑎=
3
2@½𝜔"*É+;
4
3
11mÁ2023·îÜ·ÄÅy\!
𝑓(𝑥) = cos 𝜔𝑥+ π
4 (𝜔> 0)@½q¾ŀŁÿ";Á    Å
Am‘𝑓(𝑥) = 𝑓(π−𝑥)@½𝜔"*É+†
3
2
Bm‘ć𝑓(𝑥)"9:Ĝĝ£Ğ
π
2H#ğčĘł!
@½𝜔"*É+†
3
2
Cm‘𝑓(𝑥)A π
2 ,π #$ÇØ@½0 < 𝜔≤
3
4
Dm‘𝑓(𝑥)A π
2 ,π ÆĔ& 1 H12@½0 < 𝜔<
5
4
7NO
12mÁ2024·ġÝĒľ·ÄÓÔÕÅy\!
𝑓(𝑥) = cos 2𝜔𝑥−π
6 (𝜔> 0)Az{ π
2 ,π Æ;#$"@½𝜔"*Ð
+†      
.
13mÁ2024·ġÝÝĒ·ÄÓÔÕő!
𝑓(𝑥) = 2cos 𝜔𝑥+ π
3 −1(𝜔> 0)A(0,π)Æó&šH12@½𝜔"¼
+()†      
.
14mÁ2024·ŃńÜŅņŇ·ÄÓÔÕÅy\!
𝑓(𝑥) = 2sin 𝜔𝑥+ π
6 Á𝜔> 0Å@‘∃𝑥1@𝑥2 ∈[0,π]@ļč𝑓(𝑥1)
𝑓(𝑥2) = −4@½𝜔"*É+†      
.
ê7Cň
15mÁ2023·ęÌʼnŊ·ÄÓÔÕÅy\𝜔> 1@!
𝑓(𝑥) = cos 𝜔𝑥−π
3 .
(1)ĺ𝜔= 2Ļ@B𝑓(𝑥)"#$ÇÈz{s
(2)‘𝑓(𝑥)Az{ π
6 , π
3 Æ#$@B𝜔"¼+().
      
      
16mÁ23-24 Gq·ËÌŋŌ·0ĂÅy\!
𝑓(𝑥) = 2sin 𝜔𝑥+ π
6 (𝜔> 0)m
(1)‘𝑓5π
6 + 𝑥+𝑓5π
6 −𝑥= 0@B𝜔"*É+s
(2)‘𝑓(𝑥)Az{ 0, π
3 Æ"+ð†[1,2]@B𝜔"¼+()m
17mÁ2024·ÑÒ·ÄÓÔÕÅy\!
𝑓(𝑥) = 2sin(𝜔𝑥+ 𝜑) 𝜔> 0,|𝜑|≤π
2 .
(1)‘𝑓(𝑥)"9:ōý2𝐴3π
4 ,0 @𝐵π
4 ,2 @Ï2𝐵óŎ;𝑓(𝑥)"9:8ŏŐ2𝐴*D"*2@JB𝑓(𝑥)"C
őQs
(2)‘𝑓(0) = −1@Ï𝑓(𝑥)A 5π
9 ,π Æ#$@A 0, 3π
4 Æó&šH12@B𝜔"¼+().
18mÁ2024·ÑÒ·ÄÓÔÕÅy\!
𝑓(𝑥) = 3sin(𝜔𝑥+ 𝜑) 𝜔> 0,|𝜑|< π
2 .
(1)ĺ𝜑=
π
6Ļ@!
𝑓(𝑥)A π
3 , 2π
3 Æ#$ÇÈ@BĐ
𝜔"¼+().
(2)‘𝑓(𝑥)"9:xÖ×𝑥=
π
4-.Ï𝑓−π
4 = 0@;ŒíAĐ
𝜔@ļč𝑓(𝑥)A 7π
18 , 5π
9 Æ#$œ‘íA@B
¿𝜔"+s‘¸íA@©„Ŕ.
19mÁ2023·ŕÝ·ÄÓÔÕÅy\!
𝑓(𝑥) = 𝐴sin(𝜔𝑥+ 𝜑)(𝐴> 0,𝜔> 0)"9:;Ŕ𝑦= 2sin 𝜔𝑥+ π
6 "9
:Ĝĝ£Ğ
π
6H#ğąĠčĘ".
      
      
(1)‘𝑓(𝑥)"*Éÿ/0†π@B𝑓(𝑥)"9: y žŏŐ*D"-.žŖŗs
(2)‘𝑓(𝑥)A π
2 , 3π
2 Æ&Ïä&GH12@B𝜔"¼+().