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# What's the answer to 4sin(theta)=3cos(theta), and how do you get there? Thanks!

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What's the answer to 4sin(theta)=3cos(theta), and how do you get there? Thanks!

Feb 7, 2015

#2
+94237
+10

There are two solutions on [0, 2pi]

One occurs at about (36.9, 2.4)  and the other at about (216.9, -2.4)

These solutions repeat on every 2pi interval

Here's the graph......https://www.desmos.com/calculator/xvemw185zj

Feb 7, 2015

#1
+94976
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4sin(theta)=3cos(theta)

$$\\4sin(\theta)=3cos(\theta)\\\\ \frac{sin\theta}{cos\theta}=\frac{3}{4}\\\\ tan\theta=0.75\\\\ \theta=atan(0.75)$$

$$\underset{\,\,\,\,^{{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.75}}\right)} = {\mathtt{36.869\: \!897\: \!645\: \!844^{\circ}}}$$

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Feb 7, 2015
#2
+94237
+10

There are two solutions on [0, 2pi]

One occurs at about (36.9, 2.4)  and the other at about (216.9, -2.4)

These solutions repeat on every 2pi interval

Here's the graph......https://www.desmos.com/calculator/xvemw185zj

CPhill Feb 7, 2015
#3
+94976
0

Thanks Chris.

Never forget that there is often more than one solution with trigonometry. :)

You would think I should have learned this lesson by now - I guess I haven't.  :))

Feb 7, 2015