Question

Solve for the angle θ, where 0≤θ≤2π.
cos²(θ)=1/4
θ= ??

Answer 1

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

Answer 2

+/- π/3

Answer 3

your job is to use the unit circle to see when this happens

Answer 4

\[\theta=60^o, 300^o , \theta=120^o, 240^o\]

Answer 5

myininaya where do you see degrees in this problem?

Answer 6

it is real easy to convert to degrees if you want it in degrees

Answer 7

says
\[0\leq \theta\leq2\pi\]

Answer 8

multiply by pi/180degrees

Answer 9

you do know 0 =0 degrees
and 2pi=360 degrees

Answer 10

like hell

Answer 11

lol

Answer 12

\[\sin(x),\cos(x)\] are functions of numbers. put in a number, get out a number.

Answer 13

there is no pleasing satellite

Answer 14

in this case the number is between 0 and 2 pi

Answer 15

or 0 and 360 degrees

Answer 16

hell no

Answer 17

hell yes

Answer 18

like i said if he wants to convert it to radians
he can just multiply by pi/(180degrees)

Answer 19

if i ask you to solve
\[f(x)=x^2+2x=6\] you do not ask me if x is in degrees, radians, Celsius, Fahrenheit, dollars or ruppees
x is assumed to be a real number

Answer 20

use the half angle formula

Answer 21

i'm telling the problem what i want to work with
when i give the problem my answer
i told the problem i want to work in degrees
so the problem understood

Answer 22

sine and cosine are functions of real numbers. as such they correspond to the functions of "angles" only if they are measured in radians

Answer 23

that does nothing but lead to confusion. convert, solve, convert back. terrible idea

\[\frac{\pi}{3}\] is a perfectly good number.

Answer 24

so is 60 degrees

Answer 25

no it is not it is a number

Answer 26

what?

Answer 27

i know its a number
you aren't making any sense

Answer 28

sits somewhere to the right of 1 on the number line

Answer 29

so are you saying 12 inches and 1 foot don't represent the same measurement?

Answer 30

it is like saying 0 is 32 because in celsius 0 degrees corresponds to 32 degrees farenheit

Answer 31

i am saying that sine and cosine are functions of numbers. put in a number, get out a number.

Answer 32

i agree that 1 foot equals 12 inches, but that doesn't mean that if i have a function
\[f(x)=x^2+6x\] then
\[f(1)=f(12)\]

Answer 33

f(1 foot)=f(12 inches)

Answer 34

we both agree that the derivative of sine is cosine right?

Answer 35

functions are functions of real numbers, not if degrees or radians or dollars or feet or yards or parsecs

Answer 36

what about cos²(θ)=(2+√2) / (4)

Answer 37

as such, the trig functions correspond the the high school function of angles only if the angles are measured in radians

Answer 38

this one is a pain
gimmick is to rewrite
\[\cos^2(x)\] as
\[\frac{1}{2}(\cos(2x)+1)\]

Answer 39

that will give you
\[\frac{1}{2}(\cos(2x)+1)=\frac{2+\sqrt{2}}{4}\]
\[2(\cos(2x)+1)=2+\sqrt{2}\]
\[2\cos(2x)=\sqrt{2}\]
\[\cos(2x)=\frac{\sqrt{2}}{2}\] and so
\[2x=\frac{\pi}{4}\] or
\[2x=\frac{7\pi}{4}\] etc

Answer 40

shall i divide 2x by 2??

Answer 41

yes

Answer 42

so it will be 7π/8 ,π4/8 and what are the other 2 angles