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) \(\cos(2\cdot 15^{\circ})\) ifadesi kaça eşittir?

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

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

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

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

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

4) \(\tan 15^{\circ}\) ifadesi kaça eşittir?

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

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

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

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

A) \(1\) B) \(\frac{161}{289}\) C) \(0\) D) \(\frac{1}{2}\) E) \(\frac{240}{289}\)

7) \(\cos 75^{\circ}\) ifadesi kaça eşittir?

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

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

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

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

A) \(\frac{161}{290}\) B) \(\frac{15}{17}\) C) \(\frac{161}{289}\) D) \(\frac{8}{17}\) E) \(\frac{160}{289}\)

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

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

11) \(\sin x=\frac{3}{5},\ \cos x=\frac{4}{5}\) olduğuna göre \(\cos 2x\) kaça eşittir?

A) \(\frac{7}{26}\) B) \(\frac{7}{25}\) C) \(\frac{6}{25}\) D) \(\frac{4}{5}\) E) \(\frac{3}{5}\)

12) \(2\sin x\cos(2x) = -\sin x\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

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

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

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

14) \(\sin\alpha=\frac{5}{13},\ \cos\alpha=\frac{12}{13},\ \sin\beta=\frac{8}{17},\ \cos\beta=\frac{15}{17}\) olduğuna göre \(\sin(\alpha+\beta)\) kaça eşittir?
\(0^{\circ}<\alpha,\beta<90^{\circ}\)

A) \(-\frac{21}{221}\) B) \(\frac{171}{221}\) C) \(\frac{172}{221}\) D) \(\frac{140}{221}\) E) \(\frac{220}{221}\)

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

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

16) \(\sin 15^{\circ}\) ifadesi kaça eşittir?

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

17) \(2\sin x - 2\cos x = 0\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

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

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

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

19) \(\sin\alpha=\frac{5}{13},\ \cos\alpha=\frac{12}{13},\ \sin\beta=\frac{8}{17},\ \cos\beta=\frac{15}{17}\) olduğuna göre \(\cos(\alpha+\beta)\) kaça eşittir?
\(0^{\circ}<\alpha,\beta<90^{\circ}\)

A) \(\frac{171}{221}\) B) \(\frac{220}{221}\) C) \(\frac{141}{221}\) D) \(\frac{140}{221}\) E) \(-\frac{21}{221}\)

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

A) \(\frac{63}{65}\) B) \(\frac{56}{65}\) C) \(\frac{33}{65}\) D) \(\frac{34}{65}\) E) \(\frac{16}{65}\)