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

Guest Feb 7, 2015

#2**+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

#1**+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**+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