Trigonometric Equations

Solve $\cos\theta=-0.23\$  for  $0\degree\le\theta\le360\degree$  giving answers to 1 decimal place

•  $\theta=76.6\degree,103.3\degree$  

•  $\theta=103.3\degree,256.7\degree$  

•  $\theta=76.7\degree,283.3\degree$  

•  $\theta=103.3\degree,283.3\degree$  

Solve  $\tan\theta=1.4$  for  $0\degree\le\theta\le360\degree$  giving your answer to one decimal place. 

• 
   $\theta=54.5\degree,\ 125.5\degree$ 

•  $\theta=125.5\degree,305.5\degree$  
  

•  $\theta=54.5\degree,234.5\degree$  

•  $\theta=234.5\degree,305.5\degree$  
  

Solve $\sin\theta=-0.32$  for  $0\le\theta\le2\pi$  giving your answers to 3 significant figures

•  $\theta=0.325,3.47$  

•  $\theta=3.47,5.96$  

•  $\theta=2.81,\ 5.96$  

•  $\theta=2.81,3.47$  

Solve $\sqrt{3}\cos\theta-2\sin\theta\cos\theta=0$  for  $0\le\theta\le2\pi$  

•  $\theta=\frac{\pi}{3},\frac{2\pi}{3}$  

•  $\theta=\frac{\pi}{2},\frac{3\pi}{2}$  

•  $\theta=\frac{\pi}{2},\frac{3\pi}{2},\frac{\pi}{3},\frac{2\pi}{3}$  

•  $\theta=\frac{\pi}{2},\frac{3\pi}{2},\frac{\pi}{6},\frac{5\pi}{6}$  

Solve $8\sin^2\theta+2\sin\theta-3=0$ 

for  $0\degree\le\theta\le360\degree$  giving your answers to the nearest degree

•  $\theta=49\degree,131\degree,229\degree,311\degree$  

•  $\theta=30\degree,150\degree,49\degree,131\degree$  

•  $\theta=49\degree,131\degree,210\degree,330\degree$  

•  $\theta=30\degree,150\degree,229\degree,311\degree$  

Solve $\tan\ \frac{\theta}{2}=2.1$  for  $0\le\theta\le2\pi$  giving your answers to 3 significant figures

•  $\theta=2.25$  

•  $\theta=2.25,4.27$  

•  $\theta=0.563,2.13$  

•  $\theta=0.563$  

Find the general solution of the equation

 $2\sin3\theta=\sqrt{3}$  

•  $\theta=\left(-1\right)^n\ \frac{\pi}{9}+\frac{n\pi}{3}\ \ ,\ \ n\in Z$  

•  $\theta=\left(-1\right)^n\ \ \frac{\pi}{18\ }+\frac{n\pi}{3}\ \ ,\ n\in Z$  

•  $\theta=\left(-1\right)^n\ \ \frac{\pi}{9}+n\pi\ \ ,\ \ n\in Z$  

•  $\theta=\left(-1\right)^n\ \pi+3n\pi\ \ ,\ n\in Z$  

Find the general solution of the equation  $\tan2\theta=-1$  

•  $\theta=\frac{\pi}{8}+n\pi\ \ ,\ n\in Z$  

•  $\theta=-\frac{\pi}{8}+\frac{n\pi}{2}\ \ ,\ \ n\in Z$   

•  $\theta=-\frac{\pi}{8}+n\pi\ \ ,\ \ n\in Z$  

•  $\theta=\frac{\pi}{8}+\frac{n\pi}{2}\ \ ,\ n\in Z$  

Find the general solution of  $\cos\left(\theta-10\degree\right)=1$  

•  $\theta=2n\pi-10\ \ ,\ \ n\in Z$  

•  $\theta=2n\pi+10\ \ ,\ n\in Z$  

•  $\theta=360\degree n-10\degree\ \ ,\ n\in Z$  

•  $\theta=360\degree n+10\degree\ \ ,\ n\in Z$  

Find the values of R and  $\theta$  for which  $12\cos\theta+35\sin\theta\equiv R\cos\left(\theta-\alpha\right)$  

•  $R=37\ \ ,\ \ \alpha=1.24\ rad$  

•  $R=37\ \ ,\ \ \propto=0.330\ rad$  

•  $R=47\ \ \ ,\ \ \alpha=1.24\ rad$  

•  $R=47\ ,\ \ \alpha=0.330\ rad$