Unit Circle (1 Viewer)

[pheel]

Hey all, this is my first post, and please dont flame at me, if anything, please correct me in anything i'm wrong.

Okay, I go to Ngo & Sons Tutoring, [more commonly known as Troungs]. I got put into the acceralted class, missed out on the entire Mathematical Induction Topic.

Forgot to say I'm in year 9.

Okay, Right now, for those that know him, I have Mr Mai, we are learning the unit circle. Okay, I'm hanging on there, I'm sorta understanding the topic, I can do alot of them in my head, but when it requires me to draw a unit circle, I'm completely screwed up. If anyone can explain to me?

Or I'll provide 2 questions from my homework. I've done them, but I can't draw it :S [He told us we HAVE to draw it].

B. Change the following to positive acute angles (there are two answers for each).

cos 310
tan 240

Thanks, and hopefully you can provide me a diagram

-- Pheel.

 

[nightweaver066]

Hopefully this image helps.

You do not really need to consider the unit circle. I honestly have not used or have been taught to use unit circles for the purpose of changing angles > 90 to acute angles.

For the first one, cos310, first imagine the ASTC plane (i drew it for you above) and think about which quadrant it will be in. It is in the 4th quadrant, the quadrant where only cosine is positive.

Then, you take the angle it makes with the x-axis, which will be 50 degrees. As cosine is positive and the angle is 50 degrees, the answer is cos50. Remembering that cosine and sine are complements, simply minus 50 from 90 to get sin40 as the other answer.

tan240, take the same approach. It is in the 3rd quadrant and has an angle of 60 degrees between it and the x-axis. Since it is in the third quadrant where tangent is only positive, you get tan60. Complement of tangent is cotangent, so once again subtracting 60 from 90, you get 30. So the other answer is cot30.

As they demand the unit circle, just draw the circle and draw the lines as i have done in the image and show the angles.

 

[D94]

Note the All, Sine, Tangent, Cosine for each quadrant. Because your angles (in your question) are positive, you just need to consider their own quadrant respectively.

With the first quadrant, you just have a positive angle, theta. Second, pi minus theta, third, pi plus theta, and last, 2pi minus theta. You can derive any acute angle from this.

Makes sense?

 

[such_such]

I'm in year 10 so you're probably doing the same homework as I am :L
Umm the answers are wrong for the first one (B7 in your hw) because if you shove it in your calculator, the answers are different. The real answer should be cos50 and sin40 for the first one (unless I'm looking at something else). I'll be nice and draw you a ngo and son unit circle tomorrow

 

[pencilcase]

/closed thread
this thread is misleading as it does not relate to the syllabus,said excuse is unacceptable

 

[pheel]

@ nightweaver066

Thanks for the info! makes perfect sense, and for above, what does the unit circle go if its not here? :S

@all , how "important" is the unit circle in the HSC. I mean is it a major topic, or very small, like induction?
http://community.boredofstudies.org/member.php?u=1610980795

 

[nightweaver066]

@ nightweaver066

Thanks for the info! makes perfect sense, and for above, what does the unit circle go if its not here? :S

@all , how "important" is the unit circle in the HSC. I mean is it a major topic, or very small, like induction?
http://community.boredofstudies.org/member.php?u=1610980795

The unit circle is not a topic. It's just something you consider when solving different types of problems.

E.g. Proving Pythagorean trigonometric identities and various others, use in 4U complex numbers, graphing of circles and etc.

 

[such_such]

You should use the Ngo and Son method because Sir believes the ASTC is crap. I was gonna write all these notes but then I couldn't be bothered anymore :L My scanner is poor quality so excuse me for that. Btw, on the third circle, the faint triangle is meant to be rubbed out but you can still see it, so yeah.

 

[D94]

You should use the Ngo and Son method because Sir believes the ASTC is crap. I was gonna write all these notes but then I couldn't be bothered anymore :L My scanner is poor quality so excuse me for that. Btw, on the third circle, the faint triangle is meant to be rubbed out but you can still see it, so yeah.

I don't get why that method is any better than ASTC. ASTC follows logic and when you use it for inverse angles, it makes far better sense than whatever that method is. Just because one person believes ASTC is crap, it doesn't mean you should be indoctrinated into also believing ASTC is crap. My 'Sir' reckons ASTC is the best method. It's our own prerogative and either method seems fine if you understand it. In exams, you're not going to be asked to just draw a circle; you need to think cos(310) = cos(50) right on the spot, and IMO, I can't see that method any faster than ASTC method.

 

[nightweaver066]

In my opinion, that method seems rather confusing to teach and to learn.. After a quick glimpse over it, i still don't really get the concept of it.

Perhaps you should stick to your unit circle method at tutor but use whichever method (ASTC or unit circle) you prefer outside of tutor.