Question

2sin²3Ө+3sin3Ө+1=0
Find all degree solutions.

Answer 1

let \[\sin3 \theta = x\] what does that equation become?

Answer 2

2x^2+3x+1=0

Answer 3

can you solve that for x?

Answer 4

can i use quadratic formula for that?

Answer 5

if you want, or you can factorise it

Answer 6

x=-1/2 and x=-1

Answer 7

i agree

Answer 8

:D

Answer 9

now change those solutions back to trig using what we did we had earlier

\[x = \sin 3 \theta\]

Answer 10

\[\sin 3 \theta = \frac{-1}{2} \text{ , } -1\]

Answer 11

ok

Answer 12

then what else ?

Answer 13

Now you would need to solve the \(\theta\) in each equation using the unit circle.

Answer 14

is there any other way other than the unit circle ?

Answer 15

is 70 degrees and 90 degrees are answers ?

Answer 16

The unit circle is the best way, but there are other methods.

Answer 17

2sin²3Ө+3sin3Ө+1=0
Let sin3Ө=x

so
2x^2+3x+1=0
(x+1)(2x+1)=0
so x=-1 or x=-1/2

so sin3Ө=-1 or sin3Ө=-1/2
3Ө=-90 +k360 = -30+k120 or 3Ө=270+k360=90 + k120 for sin3Ө=-1
or
3Ө=-30+k360=-10+k120 or 3Ө=210+k360=70+k120 for sin3Ө=-1/2
where k is integer

Answer 18

yeah i got 70 and 90 just like Keroro :|

Answer 19

@Keroro u think it's right ?

Answer 20

yip :) if this is high school level, its definitely correct

Answer 21

so there are only 2 answers ?

Answer 22

i thought on problems like this, always like 3 or 4 answers :|

Answer 23

Assuming that the question is to find the general solution, yes, it is only 2 answers but you must include the periods i.e. k360 etc

Answer 24

which means that there can be plenty of solutions but you know u are on the right track because you have "squared" in your question which means that at most you must have 2 answers