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Babynini
 one year ago
Solve the given equation
2cos^2(theta)+sin(theta)=1
Babynini
 one year ago
Solve the given equation 2cos^2(theta)+sin(theta)=1

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Babynini
 one year ago
Best ResponseYou've already chosen the best response.0I've gotten up to 2sin^2(theta)+sin(theta)+1=0 but cann't figure out how to factor :/

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0(2sin(theta) ? ___)(sin(theta) ? ____)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1testing what you said for my ownself: \[2(1\sin^2(\theta))+\sin(\theta)1=0 \\ \text{ by pythagorean identitiy; also subtract 1 on both sides } \\ 22\sin^2(\theta)+\sin(\theta)1=0 \\ \text{ by distribute property } \\ 2\sin^2(\theta)+\sin(\theta)+1=0 \text{ combining like terms }\] Think you left a sign off on the first term here. I'm also going to multiply 1 on both sides: \[2 \sin^2(\theta)\sin(\theta)1=0\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0ah yeah I didn't notice the 2sin^2theta was negative.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1anyways if you are doing trial factors you don't have a lot of trials here since 1 is 1(1) or 1(1)

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0wait so now what do i do for factoring =.=

freckles
 one year ago
Best ResponseYou've already chosen the best response.1if you don't like factoring much you could use the quadratic formula

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0(2sin(theta)  1)(sin(theta)+1) = 0 ?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0I think factoring is usually nicer xD

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0dangit. that wouldn't give us the right answer.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well if you want to do factoring if you multiply that out the middle term will be 2sin(theta)sin(theta which will not be sin(theta)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so which where the 1 and 1 are

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0huh? wouldn't that give the same answer?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[2 \sin^2(\theta)\sin(\theta)1=0 \\ (2 \sin(\theta)+1)(\sin(\theta)1)=0\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0which would be 2sin^2(theta)2sin(theta)+sin(theta)1=0 which is what we want yeah?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0I was confused about 2sin(theta)  sin(theta) = sin(theta) but now I see hah

freckles
 one year ago
Best ResponseYou've already chosen the best response.1no no 2sin(theta)+sin(theta)=sin(theta)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1oh did you mean to write that

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0Finals week man. Killing me.

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0K so now we have sin(theta)=1/2 and sin(theta)=1

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[2 \sin^2(\theta)\sin(\theta)1=0 \\ (2 \sin(\theta)+1)(\sin(\theta)1)=0 \\ \sin(\theta)=\frac{1}{2} \text{ or } \sin(\theta)=1 \] last equation right just a sign off on the first

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0K and sin = 1/2 at 5pi/6 and 7pi/6 ....right

freckles
 one year ago
Best ResponseYou've already chosen the best response.1can I ask if you want me to check your answers can you give me the intervals in which you want to solve them

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0hm? it just says solve the given equation. No interval.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1probably looking for all solutions then

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0so perhaps 5pi/6, 7pi/6, pi/2

freckles
 one year ago
Best ResponseYou've already chosen the best response.1ok but sin(5pi/6)=1/2 not 1/2

freckles
 one year ago
Best ResponseYou've already chosen the best response.1sin(7pi/6)=1/2 so 7pi/6 is a solution sin(11pi/6)=1/2 so 11pi/6 is a solution yep yep

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and yes sin(pi/2)=1 so pi/2 is a solution to the equation sin(u)=1

freckles
 one year ago
Best ResponseYou've already chosen the best response.1if they want all the solutions and since we are working with sin and cos just +2pi*n and say where n is an integer

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\theta=\frac{7\pi}{6}+2 \pi n \\ \theta=\frac{11\pi}{6}+2 \pi n \\ \theta=\frac{\pi}{2}+2 \pi n \\ \text{ where } n \text{ is integer }\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0Ah ok. I remember this :)
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