Free Printable Penilaian Harian 1 : Persamaan Trigonometri 1

1.

Diketahui $\tan\ x\ =-\frac{\text{24}}{\text{10}}$ dan $\cos\ y=\frac{\text{3}}{\text{}5}$ . Jika x di kuadran II dan y di kuadran IV, maka $\sin\ \left(x+y\right)\ =....$

a)

$\frac{\text{56}}{65}$

b)

$-\frac{\text{56}}{65}$

c)

$\frac{\text{65}}{56}$

d)

$-\frac{\text{112}}{56}$

e)

$\frac{\text{112}}{65}$

2.

Nilai dari $\tan\ 75^o\ \tan\ 165^o\ =\ ....$

a)

1

b)

-1

c)

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

d)

$-\frac{1}{2}\sqrt{3}$

e)

$\frac{1}{3}\sqrt{3}$

3.

Nilai trigonometri $\frac{\sin\ 86^o\ \cos\ 26^o\ -\ \cos\ 86^o\ \sin\ 26^o}{\sin\ 49^o\ \sin\ 86^o-\cos\ 49^o\ \cos\ 86^o}=\ ....$

a)

$\frac{1}{2}$

b)

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

c)

$\frac{1}{2}\sqrt{3}$

d)

$\frac{1}{2}\sqrt{6}$

e)

$\frac{1}{2}\sqrt{5}$

4.

Diketahui $\sin\alpha=\frac{4}{5},\ \cos\beta=\frac{5}{13},\ \alpha\ dan\ \beta\ di\ kuadran\ I$ , maka nilai $\cos\left(\alpha+\beta\right)\ =\ ....$

a)

$-\frac{33}{65}$

b)

$-\frac{56}{65}$

c)

$\frac{33}{65}$

d)

$\frac{56}{65}$

e)

$-\frac{65}{56}$

5.

Diketahui $\sin\alpha=\frac{2}{3},\ \cos\beta=\frac{3}{4},\ \alpha\ di\ kuadran\ II\ dan\ \beta\ di\ kuadran\ IV$ maka nilai $\sin\left(\alpha+\beta\right)=....$

a)

$\frac{6+\sqrt{35}}{12}$

b)

$\frac{6-\sqrt{35}}{12}$

c)

$\frac{12+\sqrt{35}}{12}$

d)

$\frac{35+\sqrt{6}}{12}$

e)

$\frac{\sqrt{6}+\sqrt{35}}{12}$

6.

Diketahui $\cos\left(A+B\right)=\frac{2}{3}\ dan\ \cos\left(A-B\right)=\frac{1}{2}$ , maka nilai $\tan A.\ \tan B\ =\ ....$

a)

$-\frac{\text{1}}{\text{7}}$

b)

$\frac{\text{1}}{\text{7}}$

c)

$-\frac{\text{2}}{\text{7}}$

d)

$\frac{\text{3}}{\text{7}}$

e)

$-\frac{\text{3}}{\text{7}}$

7.

Tentukan penyelesaian persamaan berikut untuk nilai $0^o\le x\le360^o$
$\cos x\ \cos20^o-\ \sin x\ \sin20^o=\frac{1}{2}$

a)

$30^o,\ 45^o$

b)

$40^o,\ 45^o$

c)

$40^o,\ 280^o$

d)

$45^o,\ 280^o$

e)

$20^o,\ 45^o$

8.

Nilai $\tan\theta$ yang memenuhi persamaan
$3\ \cos\left(\theta+\frac{\pi}{4}\right)=\cos\left(\theta-\frac{\pi}{4}\right)$

a)

$\frac{1}{2}$

b)

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

c)

$\frac{3}{4}$

d)

$\frac{1}{3}\sqrt{3}$

e)

1

9.

Diketahui suatu segitiga ABC dengan panjang sisi AC = 5 cm dan panjang sisi AB = 7 cm. Titik D terletak pada sisi AB sehingga garis CD tegak lurus pada garis AB, serta panjang CD = 4 cm. Jika $\alpha$ menyatakan sudut BAC dan $\beta$ menyatakan sudut ABC. Tentukan nilai $\sin\left(\alpha+\beta\right)+\tan\left(\alpha+\beta\right)$

a)

$\frac{7}{10}\sqrt{2}+\frac{1}{7}$

b)

$\frac{7}{10}\sqrt{2}-\frac{1}{7}$

c)

$\frac{7}{10}\sqrt{3}+\frac{1}{7}$

d)

$\frac{1}{10}\sqrt{2}+\frac{1}{7}$

e)

$\frac{1}{7}\sqrt{2}+\frac{1}{10}$

10.

Diketahui p dan q adalah sudut lancip dan $p-q\ =\ 30^o$ Jika $\cos p\sin q=\frac{1}{6}$ , nilai dari $\sin p\ \cos q=....$

a)

$\frac{1}{6}$

b)

$\frac{1}{3}$

c)

$\frac{1}{2}$

d)

$\frac{2}{3}$

e)

$\frac{5}{6}$

Penilaian Harian 1 : Persamaan Trigonometri 1

Total questions: 10

Worksheet time: 30mins

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