a cos x + b sin x = c: general solution or number of solutions

1. A.
   $x=n\pi,\ n\in\mathbb{Z}$
2. B.
   $x=2n\pi+\frac{\pi}{2}\ \text{or}\ 2n\pi,\ n\in\mathbb{Z}$
3. C.
   $x=n\pi+(-1)^n\frac{\pi}{4}-\frac{\pi}{4},\ n\in\mathbb{Z}$
4. D.
   not existing

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1. A.
   $n\pi + (-1)^n\frac{\pi}{2} + \frac{\pi}{6},\; n \in \mathbb{Z}$
2. B.
   $n\pi + (-1)^n\frac{\pi}{2} - \frac{\pi}{6},\; n \in \mathbb{Z}$
3. C.
   $n\pi + (-1)^n\frac{\pi}{4} - \frac{\pi}{3},\; n \in \mathbb{Z}$
4. D.
   $n\pi + (-1)^n\frac{\pi}{4} + \frac{\pi}{3},\; n \in \mathbb{Z}$

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1. A.
   $\theta = 2n\pi - \dfrac{\pi}{2}$ or $\theta = 2n\pi, n \in Z$
2. B.
   $\theta = n\pi - \dfrac{\pi}{2}$ or $\theta = n\pi, n \in Z$
3. C.
   $\theta = n\dfrac{\pi}{2} - \pi$ or $\theta = n\dfrac{\pi}{2}, n \in Z$
4. D.
   $\theta = 2n\pi + \dfrac{\pi}{2}$ or $\theta = n\pi, n \in Z$

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1. A.
   $3$
2. B.
   $4$
3. C.
   $6$
4. D.
   $8$

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1. A.
   $-\dfrac{8}{3}$
2. B.
   $0$
3. C.
   $\dfrac{2\sqrt{7}}{3}$
4. D.
   $\dfrac{8}{3}$

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