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anonymous
 one year ago
Could somebody help me with the question:
Find all the solutions for the equation:
cosx = 1/2
Not looking for straight answers, but verification of the answer after an explanation on how to solve? Thank you!
anonymous
 one year ago
Could somebody help me with the question: Find all the solutions for the equation: cosx = 1/2 Not looking for straight answers, but verification of the answer after an explanation on how to solve? Thank you!

This Question is Closed

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1do you have a unit circle with you?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\bf cos(x)=\cfrac{1}{2}\implies cos^{1}[cos(x)]=cos^{1}\left( \cfrac{1}{2} \right)\implies x=cos^{1}\left( \cfrac{1}{2} \right) \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmmm just notice is negative anyway \(\bf cos(x)=\cfrac{1}{2}\implies cos^{1}[cos(x)]=cos^{1}\left( \cfrac{1}{2} \right)\implies x=cos^{1}\left( \cfrac{1}{2} \right) \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The whole equation you replied with isn't showing up... @jdoe0001 But, I pulled up a unit circle.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1look at the points on the unit circle that have an x coordinate of 1/2 what are the angles that correspond to these points?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0240 degrees and 120 degrees? With the radian values being 4pi/3 and 2pi/3 respectively? @jim_thompson5910

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1those are 2 of infinitely many angle values x that make cos(x) = 1/2 true

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1add on 360 (in degree mode) or 2pi (radian mode) to get coterminal angles. You can also subtract 360 or 2pi to get other coterminal angles. There is no limit to how much you can add or subtract

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1So if you're in degree mode, then the solution set is x = 120 + 360*n or x = 240 + 360*n where n is an integer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So with the answer choices of: A. {2pi/3+npi  n = o. +/1, +/2, ... } B. {5pi/6+npi  n = o. +/1, +/2, ... } C. {5pi/6+2npi, 7pi/6+2npi  n = o. +/1, +/2, ... } D. {2pi/3+2npi , 4pi/3+2npi  n = o. +/1, +/2, ... } Would the answer be D? @jim_thompson5910

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And could you help me with 1 more?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, three actually. I think I got them correct, but just verifying. 1. For cos94cos37 + sin94sin37 (degrees) would the answer be cos57? 2. For sin8xcosx  cos8xsinx, I got (in terms of sin) sin9x 3. And for cos8xcos2x  sin8xsin2x, I got cos10x Just confused, on those, when to use (cos a + b), (cos a  b), (sin a + b), or (sin a  b)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1#1 is correct you can use a calculator to get cos(94)*cos(37)+sin(94)*sin(37) = 0.54463903501502 cos(57) = 0.54463903501502 both are equal to the same decimal value. You can also subtract the two values and you'll get 0 or very close to it

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1#2 is incorrect you use sin(AB) = sin(A)cos(B)  cos(A)sin(B)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1#3 is correct cos(AB) = cos(A)cos(B) + sin(A)sin(B)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So for#2, instead of sin9x, would it be sin7x?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can you explain when to use which identity? Like when to use the sin difference or sum, vs. the cos difference or sum? And when to use  vs +?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1when you have the two 'cos' terms together, like with cos(A)cos(B) + sin(A)sin(B), you use the cos(A+B) or cos(AB) identity

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1whatever symbol is between the cos(A)cos(B) and sin(A)sin(B) is going to be the opposite inside the cosine on the left side

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436920932555:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436920967189:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1and if you have sin mixed with cosine, like sin(2x)cos(x) + cos(x)sin(2x), then you'll use sin(A+B) or sin(AB)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436921078884:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1It comes down to recognizing the form. That happens with lots of practice and memorization. You can look up the identities on a reference sheet like this one http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf (see the "Sum and Difference Formulas" section on page 2) but sometimes the teacher won't let you have a reference sheet like that. It all depends.
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