trigonometri 4
TRANSCRIPT
![Page 1: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/1.jpg)
![Page 2: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/2.jpg)
Perbandingan TrigonometriPerbandingan Trigonometri
α
(Proyektum)
x
yr
(Proyeksi)
(Proye
ktor)
![Page 3: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/3.jpg)
PERBANDINGAN TRIGONOMETRIPERBANDINGAN TRIGONOMETRI
sisi depan sudut
sisi hipotenusasin α = =
y
r
sisi apit sudut
sisi hipotenusacos α = =
x
r
sisi depan sudut
sisi apit suduttan α =
y
x=
![Page 4: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/4.jpg)
Sudut-sudut IstimewaSudut-sudut Istimewa
~~√√3311 √√3300tan tan αα
00 √√ 22 √√3311cos cos αα
11 √√33 √√ 2200sin sin αα
9090oo6060oo4545oo3030oo00ooαα
2
1
2
1
2
1
2
1
2
1
3
1
2
1
![Page 5: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/5.jpg)
IDENTITAS
cos αsin α
tan α =
Sin2 α + cos2 α = 1
tan α1
cot α =
![Page 6: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/6.jpg)
Mencari panjang sisi segitigaMencari panjang sisi segitiga
αx
yr
sin α = y
ry = r. sin α
cos α = x
rx = r. cos α
tan α = y
xy = x.tan α
![Page 7: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/7.jpg)
![Page 8: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/8.jpg)
Contoh 1Contoh 1
Berdasarkan gambar di Berdasarkan gambar di samping. Tentukan nilai samping. Tentukan nilai dari:dari:a. sin a. sin ααb. cin b. cin ααc. tan c. tan αα
αA
C
B5 cm12
cm
13 cm
![Page 9: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/9.jpg)
PembahasanPembahasan
a. sin a. sin αα = =
αA
C
B5 cm12
cm
13 cm
r y
r x
x y
1312=
=
=
13 5
512c. tan c. tan αα = =
b. cos b. cos αα = =
![Page 10: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/10.jpg)
Contoh 2Contoh 2
Berdasarkan gambar Berdasarkan gambar di samping Tentukan di samping Tentukan nilai dari :nilai dari :a. sin a. sin ααb. cin b. cin ααc. tan c. tan αα
αA
C
B6 cm8
cm
![Page 11: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/11.jpg)
PembahasanPembahasan
a. sin a. sin αα = =
αA
C
B6 cm
8 cm
10 cm r y
r x
x y
10 8=
=
=
10 6
6 8c. tan c. tan αα = =
b. cos b. cos αα = =
BC = √ 62 + 82 = √ 100BC = 10 cm.
![Page 12: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/12.jpg)
Contoh 3Contoh 3
Perhatikan gambar di Perhatikan gambar di samping. Tentukan samping. Tentukan panjang dari AC.panjang dari AC.(sin 60(sin 6000 = 0,866) = 0,866)
600
A
C
B
10 cm
![Page 13: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/13.jpg)
PembahasanPembahasan
sin 60sin 6000 = = r y
10AC=
AC = 10 . sin 60AC = 10 . sin 6000
AC = 10 . 0,866AC = 10 . 0,866
AC = 8,66 cm.AC = 8,66 cm.600
A
C
B
10 cm
![Page 14: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/14.jpg)
Contoh 4Contoh 4
Perhatikan gambar di Perhatikan gambar di samping. Tentukan samping. Tentukan panjang dari AB.panjang dari AB.(cos 60(cos 6000 = 0,500) = 0,500)
600
A
C
B
10 cm
![Page 15: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/15.jpg)
PembahasanPembahasan
cos 60cos 6000 = = r x
10AB=
AB = 10 . cos 60AB = 10 . cos 6000
AB = 10 . 0,500AB = 10 . 0,500
AB = 5,00 cm.AB = 5,00 cm.600
A
C
B
10 cm
![Page 16: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/16.jpg)
Contoh 5Contoh 5
Perhatikan gambar di Perhatikan gambar di samping. Tentukan samping. Tentukan panjang dari AB.panjang dari AB.(tan 60(tan 6000 = 1,732) = 1,732)
600
A
C
B5 cm
![Page 17: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/17.jpg)
PembahasanPembahasan
tan 60tan 6000 = = x y
5AC=
AC = 5 . tan 60AC = 5 . tan 6000
AC = 5 . 1,732AC = 5 . 1,732
AC = 8,66 cm.AC = 8,66 cm.600
A
C
B5 cm
![Page 18: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/18.jpg)
![Page 19: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/19.jpg)
Soal - 1Soal - 1
Perhatikan gambar di Perhatikan gambar di samping, panjang BC = ….samping, panjang BC = ….(sin 53(sin 5300 = 0,799, dan = 0,799, dan cos 53cos 5300 = 0,601) = 0,601)a. 9,015 cma. 9,015 cmb. 9,105 cmb. 9,105 cmc. 11,895 cmc. 11,895 cmd. 11,985 cmd. 11,985 cm
530
B
C
A
15 cm
![Page 20: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/20.jpg)
PembahasanPembahasan
Perhatikan Perhatikan ∆∆ ABC ABC(sin 53(sin 5300 = 0,799) = 0,799)
530
B
C
A
15 cmsin 53sin 5300 = = r y
15BC=
BC = 15 . sin 53BC = 15 . sin 5300
BC = 15 . 0,799BC = 15 . 0,799BC = 11,985 cmBC = 11,985 cm
![Page 21: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/21.jpg)
JawabanJawaban
Perhatikan gambar di Perhatikan gambar di samping, panjang BC = ….samping, panjang BC = ….(sin 53(sin 5300 = 0,799, dan = 0,799, dan cos 53cos 5300 = 0,601) = 0,601)a. 9,015 cma. 9,015 cmb. 9,105 cmb. 9,105 cmc. 11,895 cmc. 11,895 cmd. 11,985 cmd. 11,985 cm
530
B
C
A
15 cm
d. 11,985 cmd. 11,985 cm
![Page 22: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/22.jpg)
Soal - 2Soal - 2
Perhatikan gambar di Perhatikan gambar di samping, panjang AB = ….samping, panjang AB = ….(sin 53(sin 5300 = 0,799, dan = 0,799, dan cos 53cos 5300 = 0,601) = 0,601)a. 9,015 cma. 9,015 cmb. 9,105 cmb. 9,105 cmc. 11,895 cmc. 11,895 cmd. 11,985 cmd. 11,985 cm
530
B
C
A
15 cm
![Page 23: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/23.jpg)
PembahasanPembahasan
Perhatikan Perhatikan ∆∆ ABC ABC(cos 53(cos 5300 = 0,601) = 0,601)
530
B
C
A
15 cmcos 53cos 5300 = = r x
15AB=
AB = 15 . cos 53AB = 15 . cos 5300
AB = 15 . 0,601AB = 15 . 0,601AB = 9,015 cmAB = 9,015 cm
![Page 24: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/24.jpg)
JawabanJawaban
Perhatikan gambar di Perhatikan gambar di samping, panjang BC = ….samping, panjang BC = ….(sin 53(sin 5300 = 0,799, dan = 0,799, dan cos 53cos 5300 = 0,601) = 0,601)a. 9,015 cma. 9,015 cmb. 9,105 cmb. 9,105 cmc. 11,895 cmc. 11,895 cmd. 11,985 cmd. 11,985 cm
530
B
C
A
15 cm
a. 9,015 cma. 9,015 cm
![Page 25: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/25.jpg)
Soal - 3Soal - 3
Perhatikan gambar di Perhatikan gambar di samping, panjang BC = ….samping, panjang BC = ….(sin 58(sin 5800 = 0,848, cos 58 = 0,848, cos 5800 = = 0,530 dan tan 580,530 dan tan 5800 = 1,600) = 1,600)a. 4,240 cma. 4,240 cmb. 6,784 cmb. 6,784 cmc. 11,800 cmc. 11,800 cmd. 12,800 cmd. 12,800 cm
580
B
C
A8 cm
![Page 26: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/26.jpg)
PembahasanPembahasan
Perhatikan Perhatikan ∆∆ ABC ABC(tan 58(tan 5800 = 1,600) = 1,600)
tan 53tan 5300 = = x y
8BC=
BC = 8 . tan 583BC = 8 . tan 58300
BC = 8 . 1,600BC = 8 . 1,600BC = 12,8 cmBC = 12,8 cm
580
B
C
A8 cm
![Page 27: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/27.jpg)
JawabanJawaban
Perhatikan gambar di Perhatikan gambar di samping, panjang BC = ….samping, panjang BC = ….(sin 58(sin 5800 = 0,848, cos 58 = 0,848, cos 5800 = = 0,530 dan tan 580,530 dan tan 5800 = 1,600) = 1,600)a. 4,24 cma. 4,24 cmb. 6,78 cmb. 6,78 cmc. 11,8 cmc. 11,8 cmd. 12,8 cmd. 12,8 cm
580
B
C
A8 cmd. 12,8 cm
![Page 28: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/28.jpg)
Soal 4Soal 4
Seorang siswa akan mengukur tinggi Seorang siswa akan mengukur tinggi sebuah pohon yang berjarak 6 meter sebuah pohon yang berjarak 6 meter dari dirinya. Ia melihat puncak pohon dari dirinya. Ia melihat puncak pohon dengan sudut elevasi 30dengan sudut elevasi 3000. Jika tinggi . Jika tinggi anak 1,6 meter, maka tinggi pohon ( anak 1,6 meter, maka tinggi pohon ( dengan pembulatan 1 desimal) dengan pembulatan 1 desimal) adalah….adalah….
![Page 29: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/29.jpg)
( sin 30( sin 300 0 = 0,500, cos 30= 0,500, cos 3000 = 0,866, dan = 0,866, dan tan 30tan 3000 = 0,577 ) = 0,577 )a. 4,8 metera. 4,8 meterb. 5,0 meterb. 5,0 meterc. 5,1 meterc. 5,1 meterd. 5,3 meterd. 5,3 meter
![Page 30: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/30.jpg)
PembahasanPembahasan
Perhatikan Perhatikan ∆∆BDE.BDE.
A
D
C
E
B
6 m
6 m300
tan 30tan 3000 = = BDDE
6DE
==
DE = 6 . tan 300
DE = 6 . 0,577
DE = 3,46 meter.
![Page 31: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/31.jpg)
Panjang DE = 3,462 meterPanjang DE = 3,462 meterTinggi anak = 1,60 meterTinggi anak = 1,60 meterTinggi pohon = 3,462 m + 1,60 mTinggi pohon = 3,462 m + 1,60 m = 5,062 meter= 5,062 meter = 5,1 meter.= 5,1 meter.Jadi, tinggi pohon adalah 5,1 meter.Jadi, tinggi pohon adalah 5,1 meter.
![Page 32: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/32.jpg)
( sin 30( sin 300 0 = 0,500, cos 30= 0,500, cos 3000 = 0,866, dan = 0,866, dan tan 30tan 3000 = 0,577 ) = 0,577 )a. 4,8 metera. 4,8 meterb. 5,0 meterb. 5,0 meterc. 5,1 meterc. 5,1 meterd. 5,3 meterd. 5,3 meter
JawabanJawaban
c. 5,1 meterc. 5,1 meter
![Page 33: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/33.jpg)
Soal 5Soal 5
Ahmad dan Bondan sedang mengamati Ahmad dan Bondan sedang mengamati sebuah tiang bendera yang tingginya 6 sebuah tiang bendera yang tingginya 6 meter. Jika Ahmad dan Bondan meter. Jika Ahmad dan Bondan memandang puncak tiang dengan sudut memandang puncak tiang dengan sudut elevasi masing-masing 37elevasi masing-masing 3700 dan 45 dan 4500 dan dan mereka berada saling berseberangan, mereka berada saling berseberangan, maka jarak keduanya (dengan pembula-maka jarak keduanya (dengan pembula-tan) adalah ….tan) adalah ….
![Page 34: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/34.jpg)
Diketahui: Diketahui: sin 37sin 370 0 =0,601, tan 37=0,601, tan 3700 = 0,753, dan = 0,753, dan sin 45 sin 4500 = 0,707, tan 45 = 0,707, tan 4500 = 1,000 = 1,000a. 14 metera. 14 meterb. 15 meterb. 15 meterc. 16 meterc. 16 meterd. 17 meterd. 17 meter
![Page 35: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/35.jpg)
PembahasanPembahasan
Sketsa gambar!
6 m
A B
C
D
370 450
![Page 36: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/36.jpg)
Perhatikan Perhatikan ∆∆ADC dan ADC dan ∆∆BDC BDC
tan 37tan 3700 = = ADCD
AD 6
==
AD = 6 : tan 37AD = 6 : tan 3700
= 6 : 0,754 = 7,95 m= 6 : 0,754 = 7,95 m
tan 45tan 4500 = = BDCD
BD 6
==
AD = 6 : tan 45AD = 6 : tan 4500
= 6 : 1 = 6,0 m= 6 : 1 = 6,0 m
![Page 37: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/37.jpg)
Jarak Ahmad ke tiang = 7,95 meterJarak Ahmad ke tiang = 7,95 meterJarak Bondan ke tiang = 6,0 meterJarak Bondan ke tiang = 6,0 meter
Jarak A ke B = 7,95 m + 6,0 mJarak A ke B = 7,95 m + 6,0 m = 13,95 meter.= 13,95 meter. = 14 meter (pembulatan).= 14 meter (pembulatan).
![Page 38: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/38.jpg)
Diketahui: Diketahui: sin 37sin 370 0 =0,601, tan 37=0,601, tan 3700 = 0,753, dan = 0,753, dan sin 45 sin 4500 = 0,707, tan 45 = 0,707, tan 4500 = 1,000 = 1,000a. 14 metera. 14 meterb. 15 meterb. 15 meterc. 16 meterc. 16 meterd. 17 meterd. 17 meter
a. 14 meter
JawabanJawaban
![Page 39: Trigonometri 4](https://reader033.vdocuments.pub/reader033/viewer/2022052118/55956d9f1a28ab850c8b4584/html5/thumbnails/39.jpg)