Question

3sin^2 theta - 7sin theta + 2 = 0 (solve the equation)
I got 1/3 and 2 as my answers but in the back of the book it says, 0.34 + 2k(pi), 2.80 + 2k(pi) any help would be appreciated!!!

Answer 1

Well, I'll check it first and see who's right :P

Answer 2

Okay, I factored it to (3sin(theta) -1) (sin(theta) - 2) and got 1/3 and 2 from that

Answer 3

Oh! You solved for sin theta, but you didnt solve for theta. You need theta xD

Answer 4

And it should be negative 1/3 and negative 2.

Answer 5

You can't just solve for sin(theta), you need the actual theta.

Answer 6

opps its suppose to be - 7sin not + 7sin haha, and I am still a little confused on how the 2.80 + 2k(pi) cam into play

Answer 7

Oh. Okay, no wonder you got positives xDD Okay, so once you get sin(theta) = something, you then need theta itself. this is done by using arcsin (inverse sin, whatever youre used to). When you need to find theta or an angle itself, you must use arc or inverse.

Answer 8

Ahhhhh!!!! I see what your saying, but how would 2 be included in the answer? I thought the ratio was from [-1,1]?

Answer 9

\[If \sin (\theta) = \frac{ 1 }{ 3 }\]
\[then \sin^{-1} (\frac{ 1 }{ 3 })= \theta \]

And you're correct, it is [-1,1], good catch :p That means that sin(theta) = 2 is useless and you ignore it.

Answer 10

Okay so you recommend just ignoring the 2.80 + 2k(pi) from the back of the book? And you were very helpful!!!!

Answer 11

Oh no, that is still an answer.

Answer 12

If you know your unit circle, you're aware that if you have pi/6 and 7pi/6, the value of sin at these points is the same, they're BOTH 1/2. So yes, you would've gotten .34 from your calculator, but there is a 2nd value, straight across from it in quadrant 2, that has the same value.