+0  
 
0
133
3
avatar

4sin(2x+30)=-2

Guest May 8, 2017
Sort: 

3+0 Answers

 #1
avatar+82 
+1

Divide both sides by 4

sin(2x+30)=−​2/4

2

 

Simplify \frac{2}{4}​4​​2​​ to \frac{1}{2}​2​​1​​

\sin{(2x+30)}=-\frac{1}{2}sin(2x+30)=−​2​​1​​

Ask: What values of 2x+302x+30 will make \sin{(2x+30)}sin(2x+30) equal -\frac{1}{2}−​2​​1​​?

2x+30=-\frac{\pi }{6},-\frac{5\pi }{6}2x+30=−​6​​π​​,−​6​​5π​​

Since sin is a periodic function, add the periodicity

2x+30=2\pi n-\frac{\pi }{6},n \in Z2x+30=2πn−​6​​π​​,n∈Z
2x+30=2\pi n-\frac{5\pi }{6},n \in Z2x+30=2πn−​6​​5π​​,n∈Z

5

 

Solve for x

x=πn−​12​​π​​−15,n∈Z

 

=====================
x=πn-​π​​/12-15,n∈Z

x=πn-​π​​/12-15,n∈Z

CupcakeShark  May 8, 2017
 #2
avatar
0

Thank you

Guest May 8, 2017
 #3
avatar+6810 
0

\(4\sin(2x+30^{\circ})=-2\\ \sin(2x + 30^{\circ}) = -\dfrac{1}{2}\\ 2x + 30^{\circ} =\arcsin (-\dfrac{1}{2})\\ 2x + 30^{\circ} = -30^{\circ}\\ 2x = -60^{\circ}\\ x = 360^{\circ}n-30^{\circ}\text{ OR }360^{\circ}n+210^{\circ}\)

MaxWong  May 8, 2017

28 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