12. Sınıf Toplam-Fark ve Yarım Açı Formülleri (Trigonometri) Ödev Hazırla

12. Sınıf – Trigonometri (Toplam-Fark ve İki Kat Açı Formülleri)

Adı Soyadı:

Sınıfı:

No:

Tarih / Puan:

1) \(3\sin x + 3\cos x = \frac{3 + 3\sqrt{3}}{2}\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

A) \(45^{\circ}\) B) \(75^{\circ}\) C) \(60^{\circ}\) D) \(15^{\circ}\) E) \(30^{\circ}\)

2) \(\sqrt{3}\sin x - 1\cos x = 0\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

A) \(30^{\circ}\) B) \(45^{\circ}\) C) \(60^{\circ}\) D) \(75^{\circ}\) E) \(15^{\circ}\)

3) \(3\sin x - 3\cos x = 0\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

A) \(75^{\circ}\) B) \(15^{\circ}\) C) \(30^{\circ}\) D) \(60^{\circ}\) E) \(45^{\circ}\)

4) \(\cos(2\cdot 60^{\circ})\) ifadesi kaça eşittir?

A) \(\frac{\sqrt{2}}{2}\) B) \(-\frac{1}{2}\) C) \(--\frac{1}{2}\) D) \(\frac{\sqrt{3}}{2}\) E) \(\frac{1}{2}\)

5) \(\sin x=\frac{8}{17},\ \cos x=\frac{15}{17}\) olduğuna göre \(\sin 2x\) kaça eşittir?

A) \(\frac{240}{289}\) B) \(\frac{24}{29}\) C) \(\frac{15}{17}\) D) \(\frac{8}{17}\) E) \(\frac{241}{289}\)

6) \(\cos 2x = 0\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

A) \(60^{\circ}\) B) \(45^{\circ}\) C) \(30^{\circ}\) D) \(15^{\circ}\) E) \(75^{\circ}\)

7) \(\cos(60^{\circ}-45^{\circ})\) ifadesi kaça eşittir?

A) \(\frac{\sqrt{3}}{2}\) B) \(\frac{\sqrt{6}-\sqrt{2}}{4}\) C) \(\frac{\sqrt{2}}{2}\) D) \(\frac{\sqrt{6}+\sqrt{2}}{4}\) E) \(\frac{1}{2}\)

8) \(\sin(45^{\circ}+30^{\circ})\) ifadesi kaça eşittir?

A) \(\frac{\sqrt{6}-\sqrt{2}}{4}\) B) \(\frac{1}{2}\) C) \(\frac{\sqrt{3}}{2}\) D) \(\frac{\sqrt{6}+\sqrt{2}}{4}\) E) \(\frac{\sqrt{2}}{2}\)

9) \(\cos(45^{\circ}-30^{\circ})\) ifadesi kaça eşittir?

A) \(\frac{\sqrt{2}}{2}\) B) \(\frac{\sqrt{3}}{2}\) C) \(\frac{\sqrt{6}-\sqrt{2}}{4}\) D) \(\frac{1}{2}\) E) \(\frac{\sqrt{6}+\sqrt{2}}{4}\)

10) \(\cos 2x = -\frac{1}{2}\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

A) \(15^{\circ}\) B) \(30^{\circ}\) C) \(60^{\circ}\) D) \(75^{\circ}\) E) \(45^{\circ}\)

11) \(\sin\alpha=\frac{3}{5},\ \cos\alpha=\frac{4}{5},\ \sin\beta=\frac{5}{13},\ \cos\beta=\frac{12}{13}\) olduğuna göre \(\sin(\alpha-\beta)\) kaça eşittir?
\(0^{\circ}<\alpha,\beta<90^{\circ}\)

A) \(\frac{63}{65}\) B) \(\frac{56}{65}\) C) \(\frac{16}{65}\) D) \(\frac{3}{13}\) E) \(\frac{33}{65}\)

12) \(\tan(2\cdot 30^{\circ})\) ifadesi kaça eşittir?

A) \(\sqrt{3}\) B) \(\frac{\sqrt{2}}{2}\) C) \(-\sqrt{3}\) D) \(\frac{1}{2}\) E) \(\frac{\sqrt{3}}{2}\)

13) \(\tan(45^{\circ}+30^{\circ})\) ifadesi kaça eşittir?

A) \(\frac{\sqrt{2}}{2}\) B) \(\frac{\sqrt{3}}{2}\) C) \(\frac{1}{2}\) D) \(2-\sqrt{3}\) E) \(2+\sqrt{3}\)

14) \(2\cos x\cos(2x) = -\cos x\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

A) \(30^{\circ}\) B) \(15^{\circ}\) C) \(60^{\circ}\) D) \(75^{\circ}\) E) \(45^{\circ}\)

15) \(\sin\alpha=\frac{3}{5},\ \cos\alpha=\frac{4}{5},\ \sin\beta=\frac{8}{17},\ \cos\beta=\frac{15}{17}\) olduğuna göre \(\cos(\alpha+\beta)\) kaça eşittir?
\(0^{\circ}<\alpha,\beta<90^{\circ}\)

A) \(\frac{36}{85}\) B) \(\frac{84}{85}\) C) \(\frac{13}{85}\) D) \(\frac{37}{85}\) E) \(\frac{77}{85}\)

16) \(\tan(45^{\circ}-30^{\circ})\) ifadesi kaça eşittir?

A) \(\frac{1}{2}\) B) \(\frac{\sqrt{3}}{2}\) C) \(2-\sqrt{3}\) D) \(\frac{\sqrt{2}}{2}\) E) \(2+\sqrt{3}\)

17) \(\tan(2\cdot 60^{\circ})\) ifadesi kaça eşittir?

A) \(\frac{\sqrt{3}}{2}\) B) \(\frac{1}{2}\) C) \(0\) D) \(-0\) E) \(\frac{\sqrt{2}}{2}\)

18) \(\cos 105^{\circ}\) ifadesi kaça eşittir?

A) \(\frac{\sqrt{3}}{2}\) B) \(\frac{\sqrt{6}}{4}\) C) \(\frac{\sqrt{2}+\sqrt{6}}{4}\) D) \(\frac{\sqrt{2}}{4}\) E) \(\frac{\sqrt{2}-\sqrt{6}}{4}\)

19) \(2\cos x\cos(2x) = -\cos x\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

A) \(45^{\circ}\) B) \(60^{\circ}\) C) \(75^{\circ}\) D) \(15^{\circ}\) E) \(30^{\circ}\)

20) \(\cos 2x = -\frac{1}{2}\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

A) \(75^{\circ}\) B) \(60^{\circ}\) C) \(15^{\circ}\) D) \(30^{\circ}\) E) \(45^{\circ}\)