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

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

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

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

3) \(\sin(5x) - \sin x = 0\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

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

4) \(4\sin x + 2\cos x = 3\sqrt{2}\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

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

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

A) \(\frac{78}{85}\) B) \(\frac{84}{85}\) C) \(-\frac{13}{85}\) D) \(\frac{36}{85}\) E) \(\frac{77}{85}\)

6) \(5\sin x + 5\cos x = \frac{5\sqrt{3} + 5}{2}\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

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

7) \(1\sin x - \sqrt{3}\cos x = 0\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

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

8) \(\sin(45^{\circ}-30^{\circ})\) 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) \(\frac{\sqrt{6}+\sqrt{2}}{4}\)

9) \(5\sin x + 5\cos x = 5\sqrt{2}\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

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

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

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

11) \(3\sqrt{3}\sin x - 3\cos x = 0\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

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

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

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

13) \(\sin(60^{\circ}-45^{\circ})\) ifadesi kaça eşittir?

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

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

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

15) \(4\sin x + 5\cos x = \frac{9\sqrt{2}}{2}\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

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

16) \(2\sin x\cos(2x) = -\sin x\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

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

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

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

18) \(2\cos x\cos(2x) = -\cos x\) ve \(0^{\circ}<x<90^{\circ}\) ise x kaçtır?

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

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

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

20) \(\sin 75^{\circ}\) ifadesi kaça eşittir?

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