Question

Need some Trig HElp

Answer 1

what do you need help with?

Answer 2

i will attach the file, give me a second

Answer 3

@dan815

Answer 4

@jim_thompson5910

Answer 5

hmm, try replacing cos^2 with 1 - sin^2

Answer 6

which attachment are you on

Answer 7

the first one...

Answer 8

\[3\sin(\theta)+3 = 2\cos^2(\theta)\]

Answer 9

ok

Answer 10

i did that

Answer 11

ok, it looks like you can factor that now if you put it in ax^2+bx+c form , with the x being sin

Answer 12

\[2\sin^2(\theta)+3\sin(\theta)+1=0\]

Answer 13

wait but this is what my equation looks like so far... is it right

Answer 14

@DanJS

Answer 15

right, from the unit circle , there is the property, sin^2 + cos^2 = 1, that is what we did

Answer 16

then just simplify that down to

Answer 17

\[2\sin^2(\theta)+3\sin(\theta)+1=0\]

Answer 18

ok got it

Answer 19

so you can factor that like usual quadratics , let v=sin(theta)

2v^2 + 3v + 1 = 0

Answer 20

ok give me a sec

Answer 21

\[(v+1)(2v+1)=0\]

Answer 22

replace v back with sin(theta)

\[(\sin \theta + 1)(2\sin \theta +1) = 0\]

Answer 23

good so far?

Answer 24

yeah

Answer 25

that is true if either of those parenthesis terms are zero, so you have

\[\sin(\theta) = -1~~~or~~~\sin(\theta) = -1/2\]

Answer 26

do you know how to figure those from the unit circle?

Answer 27

yeah, but im kind of weak in my unit circle so i might get it wrong

Answer 28

Ill tell ya, soon as you get that picture, everything clicks good...

Answer 29

ok should I gust google unit circle

Answer 30

http://www.embeddedmath.com/downloads/files/unitcircle/unitcircle-letter.pdf

Answer 31

do you want a quick rundown of it, how to determine angles

Answer 32

no i got it

Answer 33

i just needed a brush up

Answer 34

the picture is fine

Answer 35

aight, what are the answers for this one

Answer 36

the answers are -pi/2, 3pi/2, -pi/6, 7p/6

Answer 37

read the problem one more time through...

Answer 38

oh so it is just 3pi/2 and 7pi/6

Answer 39

not quite... lets look at the first one...

sin(theta) = -1

Each point on the circle is the coordinate (cos , sin) , the y coordinate is the sin of the angle...

y is -1 at 270 or 3pi/2

Answer 40

for sin(theta) = -1/2

there are 2 angle values where the y coordinate is -1/2

Answer 41

ahhhh

Answer 42

i remember taking trig and never got how angles were figured till this circle pic , after the class was over

Answer 43

radius is 1, so sin = opp/hyp = opp/1 = opp , or the y coordinate

Answer 44

ok that makes sense

Answer 45

thats helpful thanks

Answer 46

welcome

Answer 47

so the solutions to the equation are?

Answer 48

@DanJS

Answer 49

@Loser66 can you help me with my other questions