A community for students.
Here's the question you clicked on:
 0 viewing
BecomeMyFan=D
 4 years ago
cos(3x) +0.5 = 0
I wan to understand how to solve it.
BecomeMyFan=D
 4 years ago
cos(3x) +0.5 = 0 I wan to understand how to solve it.

This Question is Closed

BecomeMyFan=D
 4 years ago
Best ResponseYou've already chosen the best response.0x = .6981317008 this is the answer btw i know it, but i dont know how to get to it

QuantumModulus
 4 years ago
Best ResponseYou've already chosen the best response.0Okay, you can bring the 0.5 to the right hand side and you're left with cos(3x) = 0.5. You know, or should be familiar with the fact that the arccosine of 0.5 is 60 degrees, or pi/3 radians. So, because the value is negative, it's in the second quadrant and you can say that it's 120 degrees, or 2*pi/3 radians. Now, you're left with 3x = 2*pi/3. Divide by 3, and see the values that come out, and you should get about 0.69813... radians.

sklee
 4 years ago
Best ResponseYou've already chosen the best response.0I assume 0 < x < 2pi cos(3x)=(1/2) since we know that cos(pi/3) = 1/2 and cosine is negative in the 2nd and 3rd quadrants, we have cos(3x) = cos(2pi/3) or cos (4pi/3) or cos(2pi + 2pi/3) or cos(2pi + 4pi/3) or cos(4pi + 2pi/3) or cos(4pi + 4pi/3) = cos(2pi/3) or cos(4pi/3) or cos(8pi/3) or cos(10pi/3) or cos(14pi/3) or cos(16pi/3) Thus 3x = 2pi/3 or 4pi/3 or 8pi/3 or 20pi/3 or 14pi/3 or 16pi/3. This gives your values x between 0 and 2pi

AnwarA
 4 years ago
Best ResponseYou've already chosen the best response.0\[\cos(3x)=0.5\] so 3x is either in the 2nd or 3rd quadrant, \[3x=2\pi/3+2n \pi\] or \[3x=4\pi/3+2n \pi, n=0,1,2,...\]

sstarica
 4 years ago
Best ResponseYou've already chosen the best response.0first of all let's write down the equation in terms of cos ^_^ and you'll get : \[\cos(3x) = 0.5\] now you want to find x here, if you've noticed 3x acts as the angle in this question, so simply imagine it as theta and find the angle by doing the following: \[3x = \cos^{1} 0.5\] \[ x = [\cos^{1} (0.5)]/3 = 2\pi/9 = 40\] Correct me if I'm wrong :)

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.0cos(3x) = 1/2 ; the definition of cosine consists of parts of a triangle. It will be the "leg" that is right next to it; divided by the slanted (hypotenuse); in this case, its leg=1 and slant=2 leg^2 + (opposite leg)^2 = slanted^2 1^2 + y^2 = 2^2 1 + y^2 = 4 y^2 = 3 y=sqrt(3) or y=sqrt(3) since the leg is (1) we take that to be the Q2. as it turns out; 120 degrees has a cosine of 1/2 in Q2.... gotta go....

sstarica
 4 years ago
Best ResponseYou've already chosen the best response.0I think he wanted to solve for x, right? ._.

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.03x = 120 x=120/3 x=40

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.0180+60 = 240 3x = 240 as well 3x=240 x=240/3 x=80...

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.0figure out which one = .69813.... lol.... neither one :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.