+0  
 
0
312
3
avatar

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

Guest Feb 7, 2015

Best Answer 

 #2
avatar+81090 
+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
Sort: 

3+0 Answers

 #1
avatar+91510 
+5

4sin(theta)=3cos(theta)

 

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

 

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.75}}\right)} = {\mathtt{36.869\: \!897\: \!645\: \!844^{\circ}}}$$

Melody  Feb 7, 2015
 #2
avatar+81090 
+10
Best Answer

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
avatar+91510 
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.  :))

Melody  Feb 7, 2015

35 Online Users

avatar
avatar
avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details