Free Printable UL TURUNAN TRIGONOMETRI

1.

Hasil differensial dari $T\left(x\right)=\left(\sin x+1\right)\ \left(\sin x-2\right)$

a)

$\sin\ 2x+\cos x$

b)

$\sin2x-\sin x$

c)

$\sin2x-\cos x$

d)

$\cos2x+\cos x$

e)

$\cos2x-\cos x$

2.

$g\left(\theta\right)=\frac{1-\sin\theta}{\sin\theta-3}$

Hasil differensial dari fungsi

a)

$-\frac{2\ \cos\theta}{\left(\sin\theta-3\right)^2}$

b)

$-\ 2\ \cos\theta$

c)

$-\ 2\ \sin\theta$

d)

$2\ \sin\theta$

e)

$\frac{2\ \cos\theta}{\left(\sin\theta-3\right)^2}$

3.

$R\left(t\right)=\frac{\sin t-\cos t}{\cos t+\sin t}$

Turunan dari

a)

$1+\sin2t$

b)

$1-\sin2t$

c)

$1+\cos2t$

d)

$\frac{2}{1+\sin2t}$

e)

$-\frac{2}{1+\sin2t}$

4.

$y=\tan x-\cot x\ ,\ \frac{dy}{dx\ }\ untuk\ \ x=\frac{\pi}{4}$

a)

$\frac{1}{4}$

b)

$\frac{1}{2}$

c)

$1$

d)

$2$

e)

$4$

5.

$Turunan\ dari\ y=\sec t-\operatorname{cosec}t\ adalah....$

a)

$\sin^3t+\cos^3t$

b)

$\sin^3t-\cos^3t$

c)

$\sin^2t\ .\ \cos^2t$

d)

$\frac{1}{\left(\sin t\ .\ \cos t\right)^2}$

e)

$\frac{\sin^3t+\cos^3t}{\left(\sin t\ .\ \cos t\right)^2}$

6.

$Jika\ g\left(x\right)=\frac{\cos x+2}{\sin x}\ dengan\ \sin x\ne0.\ Nilai\ dari\ g^1\left(\frac{\pi}{2}\right)=...$

a)

-2

b)

-1

c)

0

d)

1

e)

2

7.

$Turunan\ pertama\ dari\ y=\cos\left(2x^3-x^4\right)\ adalah...$

a)

$y^1=\sin\left(2x^3-x^4\right)$

b)

$y^1=-\ \sin\left(2x^3-x^4\right)$

c)

$y^1=\left(6x^2-4x^3\right)\ \cos\left(2x^3-x^4\right)$

d)

$y^1=\left(6x^2-4x^3\right)\ \sin\left(2x^3-x^4\right)$

e)

$y^1=-\left(6x^2-4x^3\right)\ \sin\left(2x^3-x^4\right)$

8.

$Turunan\ pertama\ h\left(\theta\right)=\sec^4\left(p\theta+q\right),\ p\ne0,\ p,q\ bilangan\ real\ positif\ adalah...$

a)

$4\ p\ \sec\left(p\ \theta+q\right).\ h\left(\theta\right)$

b)

$4\ p\ \tan\left(p\ \theta+q\right).\ h\left(\theta\right)$

c)

$4\ p\ \sec^4\left(p\ \theta+q\right)\ .\ h\left(\theta\right)$

d)

$4\ p\ \tan^4\left(p\ \theta+q\right)\ .\ h\left(\theta\right)$

e)

$4\ p\ \sec^3\left(p\ \theta+q\right)\ \tan\left(p\ \theta+q\right)$

9.

$Turunan\ dari\ f\left(x\right)=x\ .\ \sin x\ .\ \cos x$

a)

$f^1\left(x\right)=\frac{1}{2}\sin2x+x\cos2x$

b)

$f^1\left(x\right)=x\sin2x+x\cos2x$

c)

$f^1\left(x\right)=x\ \sin2x+\frac{1}{2}\cos2x$

d)

$f^1\left(x\right)=\frac{1}{2}\sin2x-x\cos2x$

e)

$f^1\left(x\right)=x\sin2x-\cos2x$

10.

$Turunan\ pertama\ dari\ y=\sin^3\left(2x+3\right)\ adalah...$

a)

$-\frac{3}{2}\left(\cos\left(6x+9\right)-\cos\left(2x+3\right)\right)$

b)

$\frac{9}{4}\left(\cos\left(2x+3\right)-\cos\left(6x+9\right)\right)$

c)

$\frac{3}{4}\left(\cos\left(2x+3\right)-\cos\left(6x+9\right)\right)$

d)

$\frac{3}{4}\left(\cos\left(6x+9\right)-\cos\left(2x+3\right)\right)$

e)

$\frac{3}{2}\left(\cos\left(6x+9\right)-\cos\left(2x+3\right)\right)$

11.

$Diketahui\ y=\sqrt{1+\sin^2x}\ ,\ maka\ y^1=....$

a)

$\frac{\sin x+\cos x}{1+\sin^2x}$

b)

$\frac{\sin x+\cos x}{\sqrt{1+\sin^2x}}$

c)

$\frac{\sin x-\cos x}{1+\sin^2x}$

d)

$\frac{\sin x-\cos x}{\sqrt{1+\sin^2x}}$

e)

$\frac{\sin x\ .\cos x}{\sqrt{1+\sin^2x}}$

12.

$Jika\ r=\sqrt{\sin\theta}\ ,\ maka\ \frac{dr}{d\theta}=...$

a)

$\frac{1}{2\ \sqrt{\sin\theta}}$

b)

$\frac{\cos\theta}{2\ \sin\theta}$

c)

$\frac{\cos\theta}{2\ \sqrt{\sin\theta}}$

d)

$-\frac{\sin\theta}{2\ \cos\theta}$

e)

$\frac{2\ \cos\theta}{\sqrt{\sin\theta}}$

13.

$Jika\ f\left(x\right)=-\left(\cos^2x-\sin^2x\right),\ maka\ f^1\left(x\right)\ adalah...$

a)

$2\ \left(\sin x-\cos x\right)$

b)

$2\ \left(\cos x-\sin x\right)$

c)

$\sin x\ \cos x$

d)

$2\ \sin x\ \cos x$

e)

$4\ \sin x\ \cos x$

14.

$Jika\ f\left(x\right)=a\ \tan x+b\ x\ dan\ f^1\left(\frac{\pi}{4}\right)=3\ ,\ f^1\left(\frac{\pi}{3}\right)=9.\ Maka\ \left(a+b\right)=....$

a)

$0$

b)

$1$

c)

$\frac{\pi}{2}$

d)

$2$

e)

$\pi$

15.

$suatu\ me\sin\ diprogram\ untuk\ menggerakkan\ sebuah\ alat\ penggores\ sedemikian\ hingga\ posisi\ alat\ tersebut\ dinyatakan\ dengan\ x=3\ \cos4t\ dan\ y=2t\ \left(posisi\ dalam\ satuan\ cm\ dan\ t\ dalam\ sekon\right)\ dinyatakan\ oleh\ v=\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}\ dalam\ \frac{cm}{s}.\ Besar\ kecepa\tan\ gerak\ alat\ tersebut\ pada\ t=\frac{\pi}{2}\ adalah\ ...\ \ \frac{cm}{s}$

a)

$2$

b)

$\sqrt{13}$

c)

$6\sqrt{5}$

d)

$6\sqrt{6}$

e)

$12$

UL TURUNAN TRIGONOMETRI

Total questions: 15

Worksheet time: 47mins

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