Question

Can you help me here please? Trigo question

Answer 1

on A, you will want to factor that.

Answer 2

Think of it as 6x^2 + x - 1 = 0

Answer 3

(2cosx + 1)(3cosx - 1) =0

Set each parenthesis to 0.

2cosx + 1 = 0
2cos x = -1
cosx = -1/2

3cosx - 1=0
3cosx = -1
cosx = -1/3

Answer 4

Then you find where cosx is -1/2 and cosx = -1/3. cox is -1/2 @ 120 and 240 degrees.

Answer 5

So this is a quadratic trigo equation right?

Answer 6

But idk how to find cox = -1/3. Its not on the unit circle.

Answer 7

I think I first, I have to factor out the quadratic equation by decomposition method

Answer 8

Which would give you (2cosx + 1)(3cosx - 1) =0

Answer 9

I dont remember it, can you show me the steps to how you go that?

Answer 10

Yup! To factor A, think of it as 6x^2 + x - 1 = 0

Answer 11

okk

Answer 12

Get that so far?

Answer 13

yup

Answer 14

Do you know how to factor 6x^2 + x - 1 = 0?

Answer 15

If not, I can explain.

Answer 16

Can you explain please?

Answer 17

Ax + Bx + C = 0. Multiply A times C which is what? (Dont worry about the x's. Focus on the numbers only)

Answer 18

6

Answer 19

Correct. Now what are your factors of 6?

Answer 20

6 * 1, 2 * 3 right?

Answer 21

all the positive whole numbers smaller than six that can divide evenly into 6

Answer 22

yes

Answer 23

Now looking at ( 6 * 1 ) and ( 2 * 3 ), which one of those can you use to get B?

Answer 24

You cant get a difference of 1 between 1 and 6 can you?

Answer 25

But can you get a difference of 1 between 2 and 3?

Answer 26

You can

Answer 27

To turn B into 2 separate terms instead of 1 term by itsself.

So you have Ax^2 + Bx + Bx + C = 0

Which is 6x^2 + 3x - 2x -1 = 0

Answer 28

You went from 6x^2 + x -1 =0 to 6x^2 + 3x - 2x -1 =0.

Answer 29

Get that so far?

Answer 30

Yeah, that makes sense

Answer 31

then i group the terms right/?

Answer 32

Now group the first 2 and then the second 2.

Answer 33

yes, And then I factor

Answer 34

Well, there is 1 rule when factoring by grouping. If the 3rd term is negative you must factor out the negative.

Answer 35

so,
6x^2 + 3x - 2x -1 = 0
(6x^2 + 3x) (-2x -1)
3x(2x + 1) -1(2x+1)=0
(3x-1)(2x+1)=0

Answer 36

if you didnt factor out a negative then the parenthesis wouldn't match.

Answer 37

Okkk. that makes sense. Then you jsut add the trigo ratios

Answer 38

Well you factored that equation. Which gives you (3cos -1)(2cos +1)=0

Answer 39

THEN set each parenthesis equal to 0 and solve

Answer 40

So once we have (2cosx + 1)(3cosx - 1) =0, we write 2 equations right?
(2cosx + 1) = 0-----(1) OR
(3cosx - 1) =0-----(2)

Answer 41

and then we isolate the trig function

Answer 42

Yup, 2 equations. And yes.

Answer 43

Which gives you cosx = -1/2 and cosx = 1/3.

Answer 44

ok. That makes sense

Answer 45

Where does cos = -1/2? @ 120 and 240 degrees.

Answer 46

with that, I now determine the quadrants right?

Answer 47

But like I was saying, I dont remember how to find the degree value of cosx = 1/3

Answer 48

Well you should have your unit circle memorized.

Answer 49

since, this is cos
Equation 1 will be negative in quadrant 2 and 3

Answer 50

http://www.mathpeer.com/images/trig/unit_circle.gif

Answer 51

(cos,sin) is how it goes.

Answer 52

Yes it will:)

Answer 53

But idk about equation 2.

Answer 54

And equation 2, will be positive in quadrant 1 and 4

Answer 55

Wouldnt equation 2 be in quadrant 1 and 4?

Answer 56

Yea, But I dont know how to find the degree value. Which is probably what you need for ur answer. Unless its just asking for the quardant

Answer 57

no, It goes further than that

Answer 58

yea, it wants the exact value. Which I dont remember how to find for cosx = 1/3

Answer 59

One sec. Il ask someone

Answer 60

Alrighty. Im gonna look at the second problem.

Answer 61

Ok I asked a user, she told me the degree value for the second equation is 70.52878 or 289.4712

Answer 62

Then I guess its that

Answer 63

wait, how would we get that value?

Answer 64

Idk. You should be alble to solve it without a calc.

Answer 65

May wanna ask the teacher. (Im pretty sure im solving it correctly)

Answer 66

hmmm. Ok so first equation..

Answer 67

first equation is -1/2 right?

Answer 68

1/2 is one of the special triangle numbers

Answer 69

can the reference angle be -30degrees?

Answer 70

Oh on, cause reference angle is always positive right?

Answer 71

if the value is 1/2, the reference angle is 30degrees, what would the reference angle be for -1/2?

Answer 72

same thing? 30 degrees?

Answer 73

well for the first equation you get cosx= -1/2 which is actually 120 degrees and 240 degrees. Or 2pie/3 and 4pie/3

Answer 74

wait, how did you find that out?

Answer 75

http://www.mathpeer.com/images/trig/unit_circle.gif

Answer 76

(cos value, sine value)

Answer 77

So look where cos value is -1/2.

Answer 78

http://media.wiley.com/Lux/47/305647.image0.jpg

Answer 79

Especially if you have it memorized! Its actually simple to memorize.

Answer 80

Just gotta know how.

Answer 81

Wow. Thanks Jared, Youre like a resource vehicle!

Answer 82

wait, so those are the answers right?

Answer 83

Thank you so much Jared, Again im sorry i am really slow:), and thank you for helping me through:)

Answer 84

Should be. (if i did the problem correctly.)

But (if its correct) its only the answers for the first equation. Still gotta find cosx = 1/3

Answer 85

Thats problem A. Still gotta do problem B. Just saying

Answer 86

I know. I will consult it with someone else to double check.

Answer 87

I definitely would. My answer is either right or really really close.

well for the first equation you get cosx= -1/2 which is actually 120 degrees and 240 degrees. Or 2pie/3 and 4pie/3

Answer 88

for cosx = 1/3? idkkk..

Answer 89

Yeah. I will ask a friend of mine. Thanks again Jared:)

Answer 90

Yup. Ill see ya some other time. I need sleep my friend. byebye

Answer 91

Thank you:) Goodnight:)

Answer 92

To memorize the unit cirlce this may help.

Answer 93

hold up, im looking for it

Answer 94

http://www.foresthills.edu/userfiles/161/Classes/5071/The%20Finger%20Trick%20for%20Trig.pdf

Answer 95

Huh, That is a really handy trick:)

Answer 96

so. your pinky is 0 and your thumb is pie/2. how to find the cos of pie/3? Move that corresponding finger. whats on top is cos/2 and whats on bottom is sin/2

Answer 97

so your left with your thumb on top which is sqrt2/2 which is 1/2. on bottom your left with 3 fingers. so sqrt 3/2

Answer 98

value above the finger is cos, value below the finger is sin.