Trig question help

[Anaxogoras]

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Could there ever be a point (x, - \/3) on a unit circle?  Since r = 1, it would seem to be a contradiction, but a book I'm studying with gives negative square root 3 as a value for the y coordinate.

Here is the problem verbatim:

The ordered pair (x,y) represents a point where the terminal side of angle theta intersects the unit circle... If theta = -(pie/3), what is the value of y.

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My answer is - \/3/2.

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I'm going back to school in the Fall for a teaching credential and need to retake calculus, so this is my prep-work.

[Meatwad]

 


The answer is 42

[Serenity]

                                               _
Could there ever be a point (x, - \/3) on a unit circle?  Since r = 1, it would seem to be a contradiction, but a book I'm studying with gives negative square root 3 as a value for the y coordinate.

Here is the problem verbatim:

The ordered pair (x,y) represents a point where the terminal side of angle theta intersects the unit circle... If theta = -(pie/3), what is the value of y.

                       _
My answer is - \/3/2.

-----------------

I'm going back to school in the Fall for a teaching credential and need to retake calculus, so this is my prep-work.

God I just finished Trig this year and I don't know... wait...  there CAN be a negative radical, but your answer looks wrong... Do you not have a unit circle?

Print out this image, it will save your life in Trig studies.



edit: Your answer is exactly right. I missed the negative before the parenthesis pie/3. The tricky part is that while there can be a negative radical 3 over 2, it is NOT at pie over 3, but rather at 4pie over 3. The negative in the initial problem throws it off, but I think your answer is exactly right.

[MORAY37]

                                               _
Could there ever be a point (x, - \/3) on a unit circle?  Since r = 1, it would seem to be a contradiction, but a book I'm studying with gives negative square root 3 as a value for the y coordinate.

Here is the problem verbatim:

The ordered pair (x,y) represents a point where the terminal side of angle theta intersects the unit circle... If theta = -(pie/3), what is the value of y.

                       _
My answer is - \/3/2.

-----------------

I'm going back to school in the Fall for a teaching credential and need to retake calculus, so this is my prep-work.

Anax, unit circle will be of great value to you.

Yes, there can and will be a y value of -/3/2, in quadrant 3 and 4.



EDIT: Had posted a unit circle for you, took it down.  Serenity beat me to it.    Serenity

[Serenity]

Anax, unit circle will be of great value to you.

Yes, there can and will be a y value of -/3/2, in quadrant 3 and 4.



EDIT: Had posted a unit circle for you, took it down.  Serenity beat me to it.    Serenity

  Moray

Just got out of the subject myself (Literally, today was my very last day!).

[eagl]

I use unit circle every day when guesstimating crosswinds, same with 3-4-5 triangles, knowing that a 30/60/90 triangle has one side 1/2 the hypotenuse, etc.  Lots of other pilots wonder why my guesses are always within about 1 knot of actual headwind/crosswind components, and the answer is that I had geometry and trig in high school, early enough that I actually remember some of that stuff.

[MORAY37]

Moray

Just got out of the subject myself (Literally, today was my very last day!).

Trig was so damn bland and repetitive....

The only class I was happier to be rid of then Trig, was Calc. Funny thing is, I absolutely loved both semesters of College Physics.  I didn't really understand most of Calc till I used it in Physics... lol. Although, I took Calculus concurrent with Organic Chem in a semester of 21 credit hours... so that may have been the reason I had issues.

 Thankfully, they don't make biologists take anything higher than Calculus.  I would have never made it.

I do use statistics most every day though, for work.

[Serenity]

I use unit circle every day when guesstimating crosswinds, same with 3-4-5 triangles, knowing that a 30/60/90 triangle has one side 1/2 the hypotenuse, etc.  Lots of other pilots wonder why my guesses are always within about 1 knot of actual headwind/crosswind components, and the answer is that I had geometry and trig in high school, early enough that I actually remember some of that stuff.

Any special ideas on how to brush up on the practical geometry pilots use? I honestly don't have a mind for math, and while I had straight As in geometry, I honestly BARELY remember any of it. Hell I got a 590 in Math on my SATs

[Anaxogoras]

Yes, there can and will be a y value of -/3/2, in quadrant 3 and 4.

Ok, so the book shows the wrong answer, but I still wracked my brains for 20 minutes before I had the courage to believe it.

Thank you for the confirmation.

[Skyeho]

God I just finished Trig this year and I don't know... wait...  there CAN be a negative radical, but your answer looks wrong... Do you not have a unit circle?

Print out this image, it will save your life in Trig studies.

(Image removed from quote.)

edit: Your answer is exactly right. I missed the negative before the parenthesis pie/3. The tricky part is that while there can be a negative radical 3 over 2, it is NOT at pie over 3, but rather at 4pie over 3. The negative in the initial problem throws it off, but I think your answer is exactly right.

Also put your tan and cotan on the unit circle.  I found it helped with the "trick" questions my instructor put on the exams.

[Serenity]

Also put your tan and cotan on the unit circle.  I found it helped with the "trick" questions my instructor put on the exams.

Ooh! Good idea!

[eagl]

Any special ideas on how to brush up on the practical geometry pilots use? I honestly don't have a mind for math, and while I had straight As in geometry, I honestly BARELY remember any of it. Hell I got a 590 in Math on my SATs

It's mostly a collection of various rules of thumb.  I don't have them collected in one place, but there might be a civilian book or something out there.

I mostly use unit circle and the 60 to 1 rule.  There are a ton of applications of the 60 to 1 rule, from determining descent rate on an instrument approach to figuring bandit group range and separation on a B-scope radar picture.  Yea, you probably don't know what that means... don't worry about it, if you need it someone will tell you what it means

[Serenity]

It's mostly a collection of various rules of thumb.  I don't have them collected in one place, but there might be a civilian book or something out there.

I mostly use unit circle and the 60 to 1 rule.  There are a ton of applications of the 60 to 1 rule, from determining descent rate on an instrument approach to figuring bandit group range and separation on a B-scope radar picture.  Yea, you probably don't know what that means... don't worry about it, if you need it someone will tell you what it means

Actually, thanks to Falcon 4.0, I sorta understood that! 

[Nwbie]

I was gonna try and help you out -but then I remembered I played Football in college


 

Is that stuff actually taught in school?

[Hoarach]

Ha Nwbie it is. 

I just finished my freshmen year of college.

Im a biology/pre-med major and played/playing football.

Its kinda weird that I took Engineering calc 1 and calc 2 (dont know why I did as a biology major, some stupid registration people signed me up for it).  Engineering calc is probably one of the hardest classes to be taken and we used the unit circle maybe 1 or 2 classes and was never seen on a quiz or test.  My school doesn't curve grades and the highest grade in engineering calc was a C+, bad huh lol.