Question

Can someone check if my process is correct for this trigonometric question?

Answer 1

\[-2+\sec3\theta = 0\]

Answer 2

then \[\frac{ 1 }{ \cos 3\theta } -2=0\]

Answer 3

next \[1 = 2 \cos 3\theta\]

Answer 4

then \[\frac{ 1 }{ 2 } = \cos 3\theta\]

Answer 5

so far so good

Answer 6

okay. So then next do I go \[3\theta = 30+360k\] because the cos of 60 = 1/2

Answer 7

\[3\theta = 60*+360k\]

Answer 8

and then \[\theta = 20 +120k\]

Answer 9

yes that's it and it can also be 20 - 120k

Answer 10

Thanks!

Answer 11

jojo, don't forget about the other set of solutions.
cosine gives us a positive 1/2 in quadrant 4 as well, ya?

\[\large\rm 3\theta=300+360k\]\[\large\rm \theta=100+120k\]

Answer 12

Ah yes. I'm using the unit circle link you gave me. xP

Answer 13

oh hehe

Answer 14

Thanks for reminding me. :)