Question

Trig Help!!

Answer 1

like what?

Answer 2

What values for \[\theta(o \le \theta \le2\pi)\]

\[4\cos \theta +1=2\]
&

Answer 3

\[\cos \theta -\tan \theta \cos \theta =0\]

I have to satisfy the equations

Answer 4

first one tells you \(\cos(\theta)=\frac{1}{4}\)

Answer 5

second one tells you \(\tan(\theta)=1\)

Answer 6

That's not an option for the first. My choices are
\[\frac{ 2 \pi }{ 3 }, \frac{ 4\pi }{ 3 }\]
\[\frac{ \pi }{ 6 } , \frac{ 5\pi }{ 6 }\]
\[\frac{ 7\pi }{ 6 }, \frac{ 11\pi }{ 6 }\]
\[\frac{ \pi }{ 3 }, \frac{ 6\pi }{ 3 }\]

Answer 7

Second equation my choices are
\[0, \frac{ \pi }{ 4 }, \pi , \frac{ 5\pi }{ 4 }\]
\[\frac{ \pi }{ 4 }, \frac{ 5pi }{ 4 }\]
\[\frac{ \pi }{ 2 }, \frac{ 3\pi }{ 4 }, \frac{ 3\pi }{ 2 }, \frac{ 7\pi }{ 4 }\]
\[\frac{ \pi }{ 2 }, \frac{ 7\pi }{ 6 }, \frac{ 3\pi }{ 2 }, \frac{ 11\pi }{ 6 }\]

Answer 8

must be some mistake, because it is not likely that the cosine of any of those number is \(\frac{1}{4}\)

Answer 9

the original question before the equations is "what values for \[\theta(\theta \le \theta \le 2\pi )\] satisfy the equation"

Answer 10

Any clues at all?

Answer 11

\[4\cos (\theta) +1=2\]\[4\cos(\theta)=1\]
\[\cos(\theta)=\frac{1}{4}\] was there a typo there in the question ?

Answer 12

This is a screen shot of the equations and answers.

Answer 13

oooh i thought you said "simultaneously" like they both had to be true
two different questions !

Answer 14

also the first one is completely different

Answer 15

Ha no.

Answer 16

and how so?

Answer 17

\[4\cos(x)+1=2\cos(x)\] not \(2\)

Answer 18

\[4\cos(x)+1=2\cos(x)\iff \cos(x)=-\frac{1}{2}\] by algebra
then trig to get \(x=\frac{2\pi}{3}\) or \(x=\frac{4\pi}{3}\)

Answer 19

ok and ya sorry typo on the first one. so how would you figure the second?

Answer 20

any steps clear or not clear in that one?

Answer 21

No I got that one I see how you got the answers

Answer 22

second one factor and start with
\[\cos(x)(1-\tan(x))=0\] so
\[\cos(x)=0\] or \[\tan(x)=1\] then solve those

Answer 23

Okay, just imput the numbers given for x and they should equal 0?

Answer 24

that is one way
or you could know that \(\cos(\frac{\pi}{2})=0\) and \(\cos(\frac{3\pi}{2})=0\)

Answer 25

and also see if you know where \(\tan(x)=1\)

Answer 26

okay

Answer 27

ok I must be really dumb or over tired or something because I am not getting any correct answers... @satellite73

Answer 28

figured it out thanks for the help!