Question

cos(theta) sin(theta)+2cos(theta)=0

Answer 1

\[\Large \cos(\theta)\sin(\theta)+2\cos(\theta)=0\]

\[\Large \cos(\theta)\left[\sin(\theta)+2\right]=0\]

\[\Large \cos(\theta) = 0 \ \text{ or } \ \sin(\theta)+2=0\]


Do you see how to finish up?

Answer 2

i typed this problem in wrong there is suppose to be a 7 in front of the first cosine

Answer 3

7cos(theta) sin(theta)+2cos(theta)=0

thats the problem

Answer 4

sin range is from -1 to 1

Answer 5

\[\Large 7\cos(\theta)\sin(\theta)+2\cos(\theta)=0\]

\[\Large \cos(\theta)\left[7\sin(\theta)+2\right]=0\]

\[\Large \cos(\theta) = 0 \ \text{ or } \ 7\sin(\theta)+2=0\]

Answer 6

but when i typed it in my homework it said that -2/7, which it ask for the decimal, is -.286 and it says its wrong

Answer 7

-2/7 isn't the answer

Answer 8

i got the answers for the cos right though but i dont understand how 3.431+2kpi and 5.993+2kpi is the answer

Answer 9

\[\Large 7\sin(\theta)+2=0\]
\[\Large 7\sin(\theta)=-2\]
\[\Large \sin(\theta)=-\frac{2}{7}\]
Now use arcsine to isolate theta

Answer 10

so theta = -.290?

Answer 11

add on 2pi to that (2pi is roughly 6.28)

Answer 12

arcsin(-2/7) = -0.28975170143604


-0.28975170143604 + 2pi = 5.99343360574354


so that accounts for one of the answers

Answer 13

wait so im supposed to add 2pi even though at the end you add 2pik ?

Answer 14

the 2pi*k takes care of all coterminal angles (k is any integer)

Answer 15

`-0.28975170143604 radians` and ` 5.99343360574354 radians` are coterminal angles

Answer 16

oh i understand but how do you know to add the 2pi ?

Answer 17

because to find a coterminal angle, you add or subtract 2pi

because there are 2pi radians in a full circle

Answer 18

oh okay i understand now! thank you so much!

Answer 19

no problem