1. ## trigo equation

This seems easy but i am not quite sure ..

$\displaystyle 4\cos \frac{7}{2}\theta\cos \theta\cos \frac{1}{2}\theta=0$

For $\displaystyle 0<\theta<360$

so i think

$\displaystyle \cos \frac{7}{2}\theta=0$ , $\displaystyle \theta$= 180/7 , 540/7

$\displaystyle \cos \theta=0$ , $\displaystyle \theta$=90 , 270

$\displaystyle \cos \frac{1}{2}\theta=0$ , $\displaystyle \theta$= 180

Am i correct >

2. see the graph, i think 7 times it crossed the x-axis, more roots are missing. The graph looks symetric . . .

3. a better graph, see

4. Originally Posted by pacman
see the graph, i think 7 times it crossed the x-axis, more roots are missing. The graph looks symetric . . .
Sorry but that doesn't really help . Do you spot any mistake in my working ?

5. Hello, thereddevils!

Left out a few solutions . . .

$\displaystyle 4\!\cdot\!\cos\left(\tfrac{7}{2}\theta\right)\!\cd ot\!\cos(\theta)\!\cdot\!\cos\left(\tfrac{1}{2}\th eta\right)\:=\:0\quad\text{for }0^o\,<\,\theta\,<\,360^o$
$\displaystyle \cos\left(\tfrac{7}{2}\theta\right) \:=\:0 \quad\Rightarrow\quad \tfrac{7}{2}\theta \;=\;90^o + 180^on \quad\Rightarrow\quad \theta \:=\:\frac{180^o + 360^on}{7}$

. . For $\displaystyle n = 0,1,2,3,4,5,6$, we have:

. . . . $\displaystyle \frac{180^o}{7} \:=\:25\tfrac{5}{7}^o$

. . . . $\displaystyle \frac{540^o}{7} \:=\: 77\tfrac{1}{7}^o$

. . . . $\displaystyle \frac{900^o}{7} \:=\: 128\tfrac{4}{7}^o$

. . . . $\displaystyle \frac{1260^o}{7} \:=\: 180^o$

. . . . $\displaystyle \frac{1620^o}{7} \:=\: 231\tfrac{3}{7}^o$

. . . . $\displaystyle \frac{1980^o}{7} \:=\: 282\tfrac{6}{7}^o$

. . . . $\displaystyle \frac{2340^o}{7} \:=\: 334\tfrac{2}{7}^o$

$\displaystyle \cos(\theta) \:=\:0 \quad\Rightarrow\quad \theta \:=\:90^o,\:270^o$

$\displaystyle \cos\left(\tfrac{1}{2}\theta\right) \:=\:0 \quad\Rightarrow\quad \tfrac{1}{2}\theta \:=\:90^o + 180^on$

. . $\displaystyle \theta \:=\:180^o + 360 ^on \quad\Rightarrow\quad \theta \:=\:180^o$

6. Thanks soroban, that explain why there are 9 roots in my graph.
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