Question

which value of theta satisfies the equation 2cos^2theta - cos theta=0

Answer 1

\[cos^2(\theta)-cos(\theta)=0\]
\[cos(\theta)(cos(\theta)-1)=0\]
\[cos(\theta)=0\]
or
\[cos(\theta)=1\]

Answer 2

oooooooops
forgot the two!

Answer 3

ignore my post, or just modify with the two.

Answer 4

is there a formula to memorize forthis?

Answer 5

\[cos(\theta)(2cos(\theta)-1)=0\]
\[cos(\theta)=0\]
\[cos(\theta)=\frac{1}{2}\]

Answer 6

oh no the first part has nothing at all to do with trig

Answer 7

costheta(2costheta-1)=0
cost=0 => t=pi/2,3pi/2,... 2npi+pi/2 and 2npi+3p/2 for n=0,1,2,...
2cost-1=0 => cost=1/2 => t=pi/3,11pi/6,.... 2npi+pi/3 and 2npi+11pi/6 for n=0,1,2..

Answer 8

like solving
\[2x^2-x=0\]
\[x(2x-1)=0\]
\[x=0\]
\[x=\frac{1}{2}\]

Answer 9

oh no im confused

Answer 10

the trig part comes now.

Answer 11

oops that 11pi/6 is wrong
its 5pi/3

Answer 12

the first job is to solve for
\[cos(\theta)\]
the next step is to solve for \[\theta\]

Answer 13

the first steps have nothing at all to do with trig. no formulas, no nothing.

Answer 14

ok

Answer 15

think of \[cos(\theta)\] as x
and solve for x.
you have
\[2x^2-x=0\] and this is easy to solve

Answer 16

we get
\[x=0\] or \[x=\frac{1}{2}\]
so now \[cos(\theta)=0\] or \[cos(\theta)=\frac{1}{2}\]

Answer 17

the trig part comes now, seeing if we can find numbers for theta that will make this work.

Answer 18

can you do the next step, that is, can you find theta?

Answer 19

im not sure/

Answer 20

isnt it 0?

Answer 21

ok so first off we want to find where
\[cos(\theta)=0\]

Answer 22

http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

Answer 23

just look between 0 and 2pi first to see where cosine is 0

Answer 24

best cheat sheet. look on it to see where cosine is 0. it is not at 0, because \[cos(0)=1\]

Answer 25

then after just add 2npi for n=0,1,2,3,... blah blah

Answer 26

cos is the x correct?

Answer 27

yes we already know x=0, so therefore
\[cos(\theta)=0\] now we are looking for \[\theta\] that is we are looking for an angle (number) whose cosine is 0

Answer 28

what happens at pi/2?

Answer 29

60 defgrees

Answer 30

the very bottom of the cheat sheet i sent has all the angles associated with the unit circle, and all the coordinates. look on the unit circle to see where the first coordinate is 0

Answer 31

0,1

Answer 32

90

Answer 33

yay

Answer 34

if you are working in degrees it is 90

Answer 35

radians \[\frac{\pi}{2}\]

Answer 36

is there another between 0 and 2pi, that cosine will be zero?

Answer 37

but on my wksht theres noone of those answers.

Answer 38

yes at 270

Answer 39

whatever you prefer. so that takes care of \[cos(\theta)=0\] for the moment. now we need \[cos(\theta)=\frac{1}{2}\]

Answer 40

now that one is 60

Answer 41

yes 90 works, and 270 also works

Answer 42

or 300 degrees

Answer 43

exactly

Answer 44

or 3pi/2
now we can get cosine is 0 when we start at these angles and go around the circle again (2pi)
so the answer for cos(t)=0
is t=2npi+pi/2
and t=2npi+3pi/2

Answer 45

you are working in degrees so you have the answers.

Answer 46

that whole paragraph is still talking about the first one k?

Answer 47

theo nly answers available are pi over 6 0 pi/4 or pi/m3

Answer 48

then they are missing \[\frac{\pi}{2}\]

Answer 49

\[\frac{\pi}{3}\] works, from the cheat sheet

Answer 50

if those are your possible answers you are working in radians not degrees.

Answer 51

\[2 \cos^2 \theta- \cos \theta = 0\]

Answer 52

i know but i like using degrees better.

Answer 53

so was pi/3 the answer? vecause cos was 1/2?

Answer 54

yes

Answer 55

i semi get it,thank you

Answer 56

i guess it just asked 'which one of these is a solution"

Answer 57

did you look at the cheat sheet? because it is a good one

Answer 58

yeah which value satisfies the the equation

Answer 59

yes, it had a lot of good material thank you

Answer 60

could you helo me with my other math questions?

Answer 61

2 cos_th^2 - cos_th = 0
cos_th (2 cos_th - 1) = 0
-> cos_th =0 or 1/2
-> th = theta = +pi/2 or - pi/2 or -pi/3 or +pi/3
*

Answer 62

@LynFran