Question

what values for theta (0< theta < 2pi) satisfy the equation 2 cos theta + 1 = -cos theta

Answer 1

@Luigi0210

Answer 2

\[2\cos \theta+1=-\cos \theta\]
Move all to one side\[3\cos \theta=-1\]
\[\cos \theta=-\frac{ 1 }{ 3 }\]

Answer 3

I don't know if that's right..

Answer 4

\[2 \cos \theta + 1 = - \cos \theta\]
\[3 \cos \theta = -1\]\[\cos \theta = -\frac{ 1 }{ 3 }\]\[\theta = \cos^{-1} -\frac{ 1 }{ 3 }\]
\[\cos \theta < 0 \]
therefore is in the second and third quadrant
Use the reference angle given by :
\[\theta _{r}= \cos^{-1} \frac{ 1 }{ 3}\]
Then you have two solution
\[\pi - \theta _{r}\]
and
\[\pi + \theta _{r}\]

Answer 5

so 0 and 3.14?

Answer 6

It's whatever theta is -/+ pi, like vel showed

Answer 7

im confused.

Answer 8

Because θr is not a special case angle like 30,45,60,90 etc you need a calculator to get the number

Answer 9

Im so confused with thi questions lol sorry guys maybe because im a little sleep..

Answer 10

sleepy*

Answer 11

\[\cos^{-1} \frac{ 1 }{ 3 }=1.23\]
\[\pi =3.14\]


3.14 - 1.23

3.14 + 1.23