Math problem: 19 June 2019Prove the following trigonometric identity:(cos 2a + cos 4a + cos 6a) sin a = sin 3a cos 4a
1. Math problem: 19 June 2019Prove the following trigonometric identity:(cos 2a + cos 4a + cos 6a) sin a = sin 3a cos 4a
Identitas trigonometri
(cos 2a + cos 4a + cos 6a) sin a = sin 3a cos 4a
2 (cos 2a + cos 4a + cos 6a) sin a = 2 sin 3a cos 4a
ruas kiri
2 cos 2a sin a + 2 cos 4a sin a + 2 cos 6a cos a
= sin (2a + a) - sin (2a - a) + sin (4a + a) - sin (4a - a) + sin (6a + a) - sin (6a - a)
= sin 7a - sin a
= sin (4a + 3a) - sin (4a - 3a)
= 2 cos 4a sin 3a
= ruas kanan
Terbukti
Jawab:
Penjelasan dengan langkah-langkah:
[tex](cos2a+cos4a+cos6a)sina\\\\=(2cos(\frac{6a+2a}{2})cos(\frac{6a-2a}{2})+cos4a)sina\\\\=(2cos4a.cos2a+cos4a)sina\\\\=cos4a(2cos2a+1)sina\\\\=cos4a(2cos2a.sina+sina)\\\\=cos4a(sin(2a+a)-sin(2a-a)+sina)\\\\=cos4a(sin3a-sina+sina)\\\\=cos4a.sin3a~(terbukti)[/tex]
2. 21. Use the trigonometric identity sin 2x = 2 sin x cos x along with the Product Rule to find D, sin 2x. 22. Use the trigonometric identity cos 2x = 2 cos^2x-1 along with the Product Rule to find D, cos 2x.
Jawaban:
Jawabannya nomer 22 di atas
Penjelasan dengan langkah-langkah:
terimakasih atas pertanyaan nya
maaf jika salah yaaa
3. Tentu kan turunan pertama fungsi trigonometric Dari 1. y= 1/8 cos (4x2+3x) 2. y=sin 2x cos2 2x Plis bantuin ya soalnya besok saya mau ulangan
1. Turunan pertama fungsi y = [tex]\frac{1}{8}[/tex] cos (4x² + 3x) adalah y' = [tex]-\frac{1}{8}[/tex](8x + 3) sin (4x² + 3x) atau y' = -(x + [tex]\frac{3}{8}[/tex]) sin (4x² + 3x)
2. Turunan pertama fungsi y = sin 2x cos² 2x adalah y' = 6 cos³ 2x - 4 cos 2x
Nilai tersebut diperoleh dari perhitungan turunan pertama fungsi trigonometri dengan subtitusi.
Simak pembahasan mengenai turunan pertama fungsi trigonometri berikut.
PembahasanTurunan pertama dari beberapa fungsi trigonometri antara lain:
y = sin x → y' = cos xy = cos x → y' = -sin xy = tan x → y' = sec² xy = cot x → y' = -cosec² xy = sec x → y' = sec x.tan xy = cosec x → y' = -cosec x.cot xy = sin ax→ y' = a cos axy = cos ax → y' = -a sin axDari soal akan ditentukan turunan pertama fungsi trigonometri.
1. Turunan pertama fungsi y = [tex]\frac{1}{8}[/tex] cos (4x² + 3x)
misal:
u = 4x² + 3x
[tex]\frac{du}{dx}[/tex] = 2(4)x²⁻¹ + 3
[tex]\frac{du}{dx}[/tex] = 8x + 3
Sehingga diperoleh persamaan
y = [tex]\frac{1}{8}[/tex] cos u
Maka turunan pertama fungsi y terhadap x adalah
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{1}{8}[/tex] (-sin u) × [tex]\frac{du}{dx}[/tex]
subtitusikan kembali nilai u ke dalam fungsi
y' = [tex]-\frac{1}{8}[/tex] sin (4x² + 3x) × (8x + 3)
y' = [tex]-\frac{1}{8}[/tex](8x + 3) sin (4x² + 3x)
y' = ([tex]-\frac{1}{8}[/tex](8x) - 3[tex]\frac{1}{8}[/tex]) sin (4x² + 3x)
y' = (-x -[tex]\frac{3}{8}[/tex]) sin (4x² + 3x)
y' = -(x + [tex]\frac{3}{8}[/tex]) sin (4x² + 3x)
∴ Jadi turunan pertama fungsi y = [tex]\frac{1}{8}[/tex] cos (4x² + 3x) adalah y' = [tex]-\frac{1}{8}[/tex](8x + 3) sin (4x² + 3x) atau y' = -(x + [tex]\frac{3}{8}[/tex]) sin (4x² + 3x)
2. Turunan pertama fungsi y = sin 2x cos² 2x
Misal:
u = sin 2x
u' = 2 cos 2x
dan
v = cos² 2x
Misal a = cos 2x
[tex]\frac{da}{dx}[/tex] = -2 sin 2x
v = a²
v' = 2a × [tex]\frac{da}{dx}[/tex]
v' = 2 cos 2x (-2 sin 2x)
v' = -4 cos 2x sin 2x
Sehingga diperoleh turunan pertama fungsi y = sin 2x cos² 2x sebagai berikut
y = u.v
y' = u'v + v'u
y' = 2 cos 2x (cos² 2x) + (-4 cos 2x sin 2x)(sin 2x)
y' = 2 cos³ 2x - 4 cos 2x sin² 2x
Ingat! sin² x + cos² x = 1, maka sin² ax + cos² ax = 1
sin² ax = 1 - cos² ax
y' = 2 cos³ 2x - 4 cos 2x (1 - cos² 2x)
y' = 2 cos³ 2x - 4 cos 2x + 4cos³ 2x
y' = 6 cos³ 2x - 4 cos 2x
∴ Jadi turunan pertama fungsi y = sin 2x cos² 2x adalah y' = 6 cos³ 2x - 4 cos 2x.
Pelajari lebih lanjutMenentukan biaya produksi minimum https://brainly.co.id/tugas/23124815Menentukan kedudukan garis singgung suatu kurva https://brainly.co.id/tugas/23171337----------------------------------------Detil jawabanKelas: 11
Mapel: Matematika
Bab: Turunan fungsi aljabar
Kode: 11.2.9
Kata kunci: turunan, fungsi, trigonometri
4. The first derivative of the trigonometric function f(x) = tan x - 5 sinx is...~thank you for answering~ :):
Answer:
f'(X) = sec^x - 5 cosx
sedang tidak mood kakak??
5. saya mengukur tiang bendera orang yang A=15° Dan selanjut Nya orang yang B=45° berapa tinggi tiang bendera tersebut cara trigonometric?
Jawaban:
60
Penjelasan dengan langkah-langkah:
maaf kalau salah semoga membantu ya
6. Tentukan nilai-nilai perbandingan Trigonometric berikut. a. Sin ab.Tan ac.Cos ad.Csc a
AC²=AB²-BC²
=5²-3²=16
AC=4
a. sin a = sisi depan / sisi miring = 3/5
b. tan a = sisi depan/ sisi dekat =3/4
c. cos a = sisi dekat / sisi miring = 4/5
d. cosec a = 1 / sin a = 1/(3/5) = 5/3
7. An electronic calculator is a small, portable electronic device used to perform both arithmetic operations and complex mathematical operations. The first solid electronic calculator was created in the 1960 s, building on the extensive history of tools such as the abacus (developed around 2000 BC), and the mechanical calculator (developed in the 17th century AD). It was developed in parallel with the analog computers of the day. In addition to general purpose of calculators, there are those designed for specific markets, for example, there are scientific calculators which include trigonometric and statistical calculations. Some calculators even have the ability to do computer algebra. Graphing calculators can be used to graph functions defined on the real line, or higher dimensional Euclidean space. When was an electronic calculator create?
The first electronic calculator was created in the 1960
8. State the following trigonometric equations[tex] \cos(x + 35 ) = 0.5[/tex]35 itu degree ya.35 darjah
Jawab:
25⁰, 265⁰
Penjelasan dengan langkah-langkah:
9. tuliskan perbandingan trigonometric sinus cosinus Dan tangen Pada segitiga siku siku jika diketahui segitiga abc Dan siku siku Di A
itu jawabannya
maaf kalau salah
10. Evaluate Limit Involving Trigonometric Function
Jawaban:
0
Penjelasan dengan langkah-langkah:
[tex]lim_{x \to0} \frac{secx - 1}{x} \\ = lim_{x \to0} \frac{ \frac{1}{cosx} - 1}{x} \\ = lim_{x \to0} \frac{ \frac{1 - cosx}{cosx} }{x} \\ = lim_{x \to0} \frac{1 - cosx}{xcosx}. \frac{1 + cosx}{1 + cosx} \\ = lim_{x \to0} \frac{1 - {cos}^{2} x}{xcosx(1 + cosx)} \\ = lim_{x \to0} \frac{{sin}^{2} x}{xcosx(1 + cosx)} \\ = lim_{x \to0} \frac{sinx}{x}. \frac{sinx}{cosx} . \frac{1}{1 + cosx} \\ = 1. \frac{sin0}{cos0} . \frac{1}{1 + cos0} \\ = 1.0. \frac{1}{2} \\ = 0[/tex]
Jawab:
[tex]\displaystyle \lim_{x\to0}\frac{\sec x-1}{x}=0[/tex]
Penjelasan dengan langkah-langkah:
[tex]\displaystyle \lim_{x\to0}\frac{\sec x-1}{x}=\lim_{x\to0}\frac{\frac1{\cos x}-1}{x}\\\lim_{x\to0}\frac{\sec x-1}{x}=\lim_{x\to0}\frac{1-\cos x}{x\cos x}\\\lim_{x\to0}\frac{\sec x-1}{x}=\lim_{x\to0}\frac{1-\cos x}{x}\cdot\lim_{x\to0}\frac1{\cos x}\\\lim_{x\to0}\frac{\sec x-1}{x}=\lim_{x\to0}\frac{2(1-\cos x)}{2x}\cdot\lim_{x\to0}\frac1{\cos x}\\\lim_{x\to0}\frac{\sec x-1}{x}=\lim_{x\to0}\frac{2\sin^2\frac12x}{x}\cdot\lim_{x\to0}\frac1{\cos x}\\\lim_{x\to0}\frac{\sec x-1}{x}=\lim_{x\to0}\sin\frac12x\cdot\lim_{x\to0}\frac{2\sin\frac12x}{x}\cdot\lim_{x\to0}\frac1{\cos x}\\\lim_{x\to0}\frac{\sec x-1}{x}=\sin\frac12(0)\cdot2\cdot\frac12\cdot\frac1{\cos 0}\\\lim_{x\to0}\frac{\sec x-1}{x}=0\cdot1\cdot1\\\boxed{\boxed{\lim_{x\to0}\frac{\sec x-1}{x}=0}}[/tex]
11. 0 kurang dari sama dengan x kurang dari sama dengan 2p a.2sin (2x-p/3 ) - akar 3=0 b.tan (3x+p/12)+1=0 Materi simple trigonometric equation
jawabannya adl matematika 20,15
12. matematika trigonometric ratios tolong dijawab ini dikumpul besok
Jawaban:
Cari pakek otak ya maaf gak bisa bantu susah pake compete:)
13. An electronic calculator is a small, portable electronic device used to perform both arithmetic operations and complex mathematical operations.The first solid electronic calculator was created in the 1960 s, building on the extensive history of tools such as the abacus (developed around 2000 BC), and the mechanical calculator (developed in the 17th century AD). It was developed in parallel with the analog computers of the day.In addition to general purpose of calculators, there are those designed for specific markets, for example, there are scientific calculators which include trigonometric and statistical calculations. Some calculators even have the ability to do computer algebra. Graphing calculators can be used to graph functions defined on the real line, or higher dimensional Euclidean space.According to the text, what is the usage of calculator?
Jawaban:
The usage of calculator can be variously in terms of the system we used. But the main usage of calculator is to help human to understand mathematical diffuculties in many ways, such as algebra, statistic, or arithmatic. It allows us to count a very simple or even complex data with a tools that are already existed long way ago and still managed to help us so much until these days.
14. kak..pliss jawab dong...important!plisss find the trigonometric function of the graph. jawab yaa :
Jawab:
4 tan x°
Penjelasan dengan langkah-langkah:
perhatikan bahwa di kuadran I (sudut 0° sampai 90°) nilai sudutnya positif, maka fungsi trigonometri yang digunakan adalah sinus atau tangen
lalu pada sudut 90° sampai 180° (kuadran II) nilai nya negatif, maka fungsi trigonometri diatas cosinus atau tangen
dari kedua kesimpulan diatas, maka jelas fungsi yang dipakai adalah tangen. perhatikan bahwa
tan 45° = 1
maka
4 tan 45° = 4
maka kemugkinan fungsi diatas berbentuk
4 tan x°
cek
4 tan 135° = 4 tan (180° - 45°) = 4 (-tan 45°) = 4.(-1) = 4×(-1) = -4 (sesuai)
4 tan 225° = 4 tan (180 + 45°) = 4 tan 45° = 4×1 = 4 (sesuai)
Jadi fungsi trigonometri yang dipakai adalah 4 tan x°
15. 15. what is the main idea of paragraph 3?. a. electronic calculators are vary b. there are many kinds of calculators based on the purpose c. scientific calculators are trigonometric and statistic d. calculators are designed for specific markets 16. what is the meaning of “extensive” in the second paragraph?. a. big b. loyal c. inside d. large 17. from the text we can conclude that calculator is very ... device in our lives. a. expensive b. helpful c. unusual d. useless answer with correctly pls
Jawaban:
15.c. scientific calculators are trigonometric and statistic
16.b. loyal
17.b. helpful
Penjelasan:
I hope this helps
16. Tentukan perbandingan trigonometric lainnya Dari soal berikut : 3 tan²B = 1, (kuadran II)
Bab Trigonometri
Matematika SMA Kelas X
3 tan² B = 1
tan² B = 1/3
tan B = - 1/3 √3 → kuadran II
B = 150°
sin 150° = 1/2
cos 150° = -1/2 √3
17. ##Quiz #103 ##• english version• big point• easy==========Determine the solution set of the trigonometric equation:2 cos(3x) +1 = 0for 0≤ x 2π
[tex]\begin{array}{rcl}2.\cos~3x+1&=&0\\~\\2.\cos~3x&=&-1\\~\\\cos~3x&=&-\frac{1}{2}\\~\\3x=\frac{2\pi}{3}&or&3x=\frac{4\pi}{3}\end{array}[/tex]
[tex](~i~)~3x=\frac{2\pi}{3}~:[/tex]
[tex]\begin{array}{rcl}3x&=&\frac{2\pi}{3}+k.2\pi\\~\\x&=&\frac{2\pi}{9}+k.\frac{2\pi}{3}\end{array}[/tex]
[tex]\to k=0~\to x=\frac{2\pi}{9}+0=\boxed{\frac{2\pi}{9}}[/tex]
[tex]\to k=1~\to x=\frac{2\pi}{9}+\frac{2\pi}{3}=\boxed{\frac{8\pi}{9}}[/tex]
[tex]\to k=2~\to x=\frac{2\pi}{9}+\frac{4\pi}{3}=\boxed{\frac{14\pi}{9}}[/tex]
[tex]\to k=3~\to x=\frac{2\pi}{9}+2\pi=\frac{20\pi}{9}[/tex]
(not a solution, because out of [tex]0\leq x\leq 2\pi)[/tex]
[tex](~i~)~3x=\frac{4\pi}{3}~:[/tex]
[tex]\begin{array}{rcl}3x&=&\frac{4\pi}{3}+k.2\pi\\~\\x&=&\frac{4\pi}{9}+k.\frac{2\pi}{3}\end{array}[/tex]
[tex]\to k=0~\to x=\frac{4\pi}{9}+0=\boxed{\frac{4\pi}{9}}[/tex]
[tex]\to k=1~\to x=\frac{4\pi}{9}+\frac{2\pi}{3}=\boxed{\frac{10\pi}{9}}[/tex]
[tex]\to k=2~\to x=\frac{4\pi}{9}+\frac{4\pi}{3}=\boxed{\frac{16\pi}{9}}[/tex]
[tex]\to k=3~\to x=\frac{4\pi}{9}+2\pi=\frac{22\pi}{9}[/tex]
(not a solution, because out of [tex]0\leq x\leq 2\pi)[/tex]
The solution set is :
[tex]\huge \boxed{\boxed{x=\begin{array}{l}\left\{\frac{2\pi}{9}~,~\frac{4\pi}{9}~,~\frac{8\pi}{9}~,\right.\\~\\\left.~\frac{10\pi}{9}~,~\frac{14\pi}{9}~,~\frac{16\pi}{9}\right\}\end{array}}}[/tex]
18. trigonometric ratio tolong bantuan
Penjelasan dengan langkah-langkah:
1. <x= 58°, < z = 90° maka segitiga siku siku
maka < y= 180°-148°= 32°
maka x/ sin x = y / sin y
dimana x = YZ
dimana y = XZ= 4,9=5 m
maka x/ sin 58°= 5/ sin 32°
arc sin 58= 0,84
arc sin 32= 0,52
maka x/ 0,84= 5/0,52
x= 8,07--> 8 m
maka XY= √ 5²+8²=√25+64= √89 ✓
2.sama seperti no 1
maka < a= 43°
maka a/ sin a= b/ sin b
AC/ sin 43°= BC / sin 47°
maka AC /0,68= BC/ 0,73
0,73 AC = 0,68 BC
AC/ BC= 0,68/0,73
AC/ BC= 0,93
maka AC = 0,93 BC
maka AC²+BC²= 324
(0,93 BC)²+BC²=324
2BC²= 323
BC²= 161,5
maka BC= √162= 12,7 atau 13 m ✓
19. Determine the value of Ax, Ay, and A! Use the trigonometric concepts to do it
Penjelasan dengan langkah-langkah:
Determine the value of Ax, Ay, and A! Use the trigonometric concepts to do it
A+A
= 7+7
= 0 ÷ y
= 672.
20. 1. Use a calculator to find each of the following angles, given its trigonometric ratio.(a) sin A = 0.527(b) cos B = 0.725 (c) tan C = 2.56 bantu plss
Jawab:
(a) sin A = 0.527
arc sin ( 0.527 ) = 31.8° ⇒ 32°
(b) cos B = 0.725
arc cos ( 0.725 ) = 43.5°
(c) tan C = 2.56
arc cos ( 2.56 ) = 68.6° ⇒ 69°
semoga membantu ;)
 sin a = sin 3a cos 4a Daftar Isi...){kind=link}
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