Aku n MATEMATIKA cah SMA Nda: Soal-Soal 3gonome3 kls XI Ipa

$1.Jika\: sin x -cosx=p\: \: maka \: sin\: 2x=....$
Jawab : sin x - cos x = p ( kedua ruas dikuadratkan )
$\left (sin \: x -cos\: x \right )^{2}=\left (p \right )^{2}$
   $sin^{2} \: x -2.sin\: x\: cos\: x +cos^{2}x=p ^{2}$
$sin^{2} \: x +cos^{2}x-2.sin\: x\: cos\: x =p ^{2}$
$1-sin\: 2x=p ^{2}$
$1-p ^{2}=sin\: 2x$

$2.\: Sederhanakan \: \: cos(60^{0}-3x).cos(60^{0}+3x)+sin(60^{0}-3x).sin(60^{0}+3x)$

Jawab :
   $cos{\color{Red} (60^{0}-3x)}.cos{\color{Magenta} (60^{0}+3x)}+sin{\color{Red} (60^{0}-3x)}.sin{\color{Magenta} (60^{0}+3x)}$
   $cos\left ({\color{Red} (60^{0}-3x)}-{\color{Magenta} (60^{0}+3x)} \right )=cos(-6x)=cos\: 6x$
$3.\: Diketahui\: tg\: a=\frac{5}{12},a\: sudut \: lancip$
$sin\: b=0,28\: ,b\: sudut \: tumpul$
$nilai\: sin(a+b)=....$
Jawab :
$sin\: a=\frac{5}{13}\: \: dan\: \: cos\: a=\frac{12}{13}$
$sin\: b=0,28=\frac{7}{25}\: ,cos\: b=-\frac{24}{25}$
Catatan : gunakan Triple Pythagoras
masing-masing nilai masukin ke rumus
$sin(a+b)=sin\: a.cos\: b-cos\: a.sin\: b$
$4.\: Bila \: A,\: B \: dan \: C \: adalah \: titik \: sudut \: segitiga\: maka\: nilai\: \frac{cos(\frac{A+B}{2})}{sin(\frac{C}{2})}=....$
Jawab : A+B+C = 180 maka sesuai soal A+B = 180 - C
trus dibagi 2 n kedua ruas kita kasi cos ......n sekarang berarti menjadi
$cos(\frac{A+B}{2})=cos(\frac{180-C}{2})=cos(90-\frac{C}{2})=sin(\frac{C}{2})$
jadi jawabane = 1

$5.\: (sin^{2}x).\left (cos^{2} x \right )=....$
$A.\:\: \frac{1}{4}+\frac{1}{4}.cos\: 2x$
$B.\:\: \frac{1}{4}-\frac{1}{4}.cos\: 2x$
$C.\:\: \frac{1}{8}+\frac{1}{8}.cos\: 4x$
$D.\:\: \frac{1}{8}-\frac{1}{8}.cos\: 4x$
$E.\:\: \frac{1}{16}+\frac{1}{16}.sin\: 2x$
$6.\: \: cos^{2}10^{0}+cos^{2}20^{0}+cos^{2}30^{0}+cos^{2}40^{0}+....cos^{2}90^{0}=....$
A. 2 B. 3 C. 4 D. 5 E. 6
$7.\: \: jika \: \: cos(x+\frac{\pi }{4})=cos(x-\frac{\pi }{4})\: \: maka :$
$A.\: \: tg\: x= \frac{1 }{3}$
$B.\: \: cos\: x= \frac{1 }{2}\sqrt{3}$
$C.\: \:tg\: x= 3$
$D.\: \:sin\: x= \frac{\sqrt{2}}{2}$
$E.\: \:sin\: x= \frac{\sqrt{3}}{2}$
$8.\: \; Nilai\: dari\: \:sin\: 75^{0}.cos\: 15^{0}+cos\: 65^{0}.cos\: 35^{0}+sin\: 10^{0}=....$
   $A.\: -\frac{1}{2}\; \; \; \; B.\: -\frac{\sqrt{3}}{2}\; \; \; \; C.\: -\frac{1}{4}\; \; \; \; D.\:\: \: \frac{\sqrt{2}}{4}\; \; \; \; E.\: \frac{\sqrt{3}}{4}$
$9.\: Jika\: cos\: 2x-cos\: x-2=0\: \: maka\: \: tg\: x=....$

$Untuk\; 0^{0}<x<360^{0}\; tentukan\; nilai\; x\; dari\; persamaan\; berikut$

$10.\;\; \: \; 2.cos\;2x- 3.sin\; x+3=0$
$11.\;\; \: \; sin\;x+ tg\; x=sin\: 2x$
$12.\;\; \: \; 4.sin\;2x-3.\left (tg\; x +ctg\: x \right )=5$
$13.\;\; \: \; 2.sin\;\left (x+30^{0} \right ).cos\: x =\frac{3}{2}$
$14.\;\; \: \; 2.cos\;\left (x+60^{0} \right ).cos\: x =1$
$15.\;\; \: \; cos\;\left (x+60^{0} \right ).cos\: x =cos\;\left (2x+60^{0} \right )+cos\: 60^{0}$
$16.\;\; \: \; sin\;3x-sin\: x=sin\: 2x$
$17.\;\; \: \; cos\;2x-cos\: x=cos\: 3x$
$18.\;\; \: \; sin\;3x-cos\: 3x=sin\;x-cos\: x$
$19.\;\; \; \frac{sin\: x}{cos\: 2x}-sin\: x=cos\: x-\frac{cos\: x}{sin\: 2x}$

Aku n MATEMATIKA cah SMA Nda

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Rabu, Oktober 19, 2011

Soal-Soal 3gonome3 kls XI Ipa

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