Solving Trig Equations (Basic)

What part of the unit circle is $\left[0,\ 2\pi\right]$ ?

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What part of the unit circle is $\left[0,\ \pi\right]$ ?

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What part of the unit circle is $\left[\frac{\pi}{2},\ \frac{3\pi}{2}\right]$ ?

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Solve: 2sinx-1=0; [ 0, 2 $\pi$ ]

•  $\frac{1}{2}$  

•  $\frac{\pi}{6},\ \frac{5\pi}{6}$  

•  $\frac{\pi}{3},\ \frac{5\pi}{3}$  

•  $\frac{\pi}{6},\ \frac{5\pi}{6},\ \frac{7\pi}{6},\ \frac{11\pi}{6}$  

Solve:  $5\tan x+3=6\tan x+4;\ \left[0,\ \pi\right]$  

• -1

•  $\frac{3\pi}{4}$  

•  $\frac{3\pi}{4},\frac{7\pi}{4}$  

•  $\frac{\pi}{4},\frac{3\pi}{4},\ \frac{5\pi}{4},\frac{7\pi}{4}$  

Solve:  $2\cos x+5\sqrt{2}=6\sqrt{2};\ \left[0,\ 2\pi\right]$  

•  $\frac{\sqrt{2}}{2}$  

•  $\frac{\pi}{4},\ \frac{7\pi}{4}$  

•  $\frac{\pi}{4},\ \frac{3\pi}{4}$  

•  $\frac{\pi}{4}$  

Solve: 2sinx=2;  $\left[0,\ 2\pi\right]$  

• 1

•  $\frac{\pi}{2}$  

•  $2\pi$  

• Not Possible

Solve:  $-3\csc x+7=13;\ \left[0,\ 2\pi\right]$  

•  $-2$  

•  $-\frac{1}{2}$  

•  $\frac{7\pi}{6},\ \frac{11\pi}{6}$  

•  $\frac{2\pi}{3},\ \frac{4\pi}{3}$  

Solve:  $4\tan x-1=2\tan x+1;\ \left[\frac{3\pi}{2},\ 2\pi\right]$  

• 1

• Not Possible

•  $\frac{\pi}{4},\ \frac{5\pi}{4}$  

•  $\frac{\pi}{4},\ \frac{3\pi}{4},\ \frac{5\pi}{4},\ \frac{7\pi}{4}$  

Solve:  $5\cos x+3\sqrt{3}=3\cos x+4\sqrt{3};\ \left[0,\ \pi\right]$  

•  $\frac{\sqrt{3}}{2}$  

•  $\frac{\pi}{6}$  

•  $\frac{\pi}{3}$  

•  $\frac{\pi}{6},\ \frac{11\pi}{6}$