Tuesday, September 11, 2007

Unit Circle!

Hey folks sorry for waiting, i`m a having a really bad technical error today. Anyways today's class started with Mr. K asking each and everyone of us if we read the post about 'Student Made This'. Then he gave us four questions to answer.

1. In which quadrant is P(5) found?

Quadrant IV

->P(5) lies on quadrant IV beacause
QI is between 0-~1.5708
QII is between ~1.5708 - ~ 3.1416
QIII is between ~3.1416 - ~~4.7124
QIV is between ~4.7124 - ~6.2832

2. State a positive coterminal angel for -π/3?

-> 5π/3 is a positive coterminal angle of -π/3
coterminal angle = given angle ± 2π
(-π/3 )+ 2π = 5π/3
5π/3 and -π/3 has the same initial and terminal side.

3. In which quadrant is
sin θ <> 0?

Quadrant IV

Quadrant I sin θ > 0 and cos θ > 0

Quadrant II sin θ > 0 and cos θ <>

Quadrant III sin θ <>

Quadrant IV sin θ <> o

4. In which quadrant is
csc θ <> 0?

Quadrant IV

Quadrant I csc θ > 0 and sec θ > 0

Quadrant II csc θ > 0 and sec θ <>

Quadrant III csc θ <0>

Quadrant IV csc θ <> o

After doing those problems, Mr. K introduced to us the other 3 trigonometric functions. So we now know 6 trig functions: sine, cosine, tangent, cosecant, secant, and cotangent.

sin θ = opp/hyp.............................csc θ = hyp/opp

cos θ = adj/hyp..............................sec θ = hyp/adj

tan θ = opp/adj..............................cot θ = adj/opp

Mr. K finally told us the story about the guy who died because of a triangle. He said that the Pythagorean believed that everything in the world are made up of whole number ratios. Mr. K also said that a student of Pythagoras not himself discovered the pythagorean theorem. He also mentioned the `3-4-5 Triangle` and the triangle that has two legs that is equal to 1 units and has a hypotenuse of square root of 2 which we have in our geometry sets.

We also did two more exercises:

1. P(θ) lies on a ray that contains the point (5,12) find the coordinates of P(θ).

a^2 + b^2 = c^2
(5^2) + (12^2) = c^2
169 = c^2
13 = c

cos θ = adj/hyp
cos θ = 5/13

sin θ = opp/hyp
sin θ = 12/13

2. List the values of all the six trigonometric ratios for P(θ)

sin θ = 12/13

cos θ = 5/13

tan θ = 12/5

csc θ = 13/12

sec θ = 13/5

cot θ = 5/12

The class finished off with Mr. K telling us to memorize the unit circle, it`s cosine and sine and it`s radians values.

At last! My scribe post is done. Memorize the unit circle and be ready for our mental math tomorrow! Remember always be on time! One more thing don`t forget to read the post about the `Student Made This`

The next scribe is rosselle...


oliver_796 said...


Mr. H said...

Dear Pre-Cal and "Cool Guy". This is a wonderful post. It does everything that a scribe post needs... diagrams, facts and a retelling of the day in a colourful way.

This post is an example to the rest of the scribes and sets the bar high early in the semester.

Keep on scribing.

Mr. Harbeck
Sargent Park School

xxcool-guyxx said...

thank you sir!