September 29, 2006

Finding the Quadrants of Trig

Hi it's me Ben. Today in class we had to work on two worksheets because unfortunately Mr. K was off to a Math workshop :-( Our substitute got us started by helping us with the first few questions on the first worksheet. Here's what he explained:

The first question ask for the values of Θ on the interval 0°≤
Θ ≤ 360° for the following questions and I have added a picture to help understand:
A)sin
Θ<0>Θ>0
B)sinΘ>0 and cosΘ≤0
C)tanΘ>0
D)cos
Θ≤0

Quadrant I:
sin
Θ›O
cos
Θ›O
tan
Θ›O
Reason: The value/ratio of sin, cos, tan is positive therfore in the 1st quadrant

Quadrant II:
sin
Θ›O
cos
Θ‹O
tan
ΘO
Reason: The value/ratio of sin
Θ is positive while cosΘ and tanΘ are negative

Quadrant III:
sin
Θ‹O
cos
Θ‹O
tan
Θ›O
Reason: The value/ratio of sinΘ and cosΘ is negative while tanΘ is positive

Quadrant IV:
sin
Θ‹O
cos
Θ›O
tan
Θ‹O
Reason: The value/ratio of sinΘ and tanΘ is negative while cosΘ is positive

The question is asking which quadrant is each condition found so:
A) sin
Θ‹O and cosΘ›O
Answer: Quadrant IV because sinΘ is negative and cosΘ is positive and the only quadrant where that happens is in quadrant IV

B)sin
Θ>O and cosΘ≤O
Answer: Quadrant II because sin
Θ is positive and cosΘ is negative and the only quadrant where that is true is in quadrant II

C)tan
Θ>O
Answer: Quadrant I and III because the only quadrant where that is true is in quadrant I and III

D)cos
Θ≤O
Answer: Quadrant II and III because that only quadrant where that is true is in quadrant II and III

The next thing he explained helped us remember what each variable of the Sin/Cos Wave Formula stood for:

y=A sin B (x-C) +D
y=A cos B(x-C) +D

A-The A represents the amplitude or the direction of opening
B- The B tells us how much the wave is horizontally compressed but unfortunately B is taught in grade 12 not in grade 11
C- The C represents the Phase Shift which tells us the horizontal shift or how far the wave is moved on the x-axis
D- The D represents the Sinusoildal Axis which tells us the vertical shift or how far the wave is moved on the y-axis

With that information in mind we were able to finish the second work sheet which told us to state the amplitude, vertical shift, and horizontal shift.

Well that's my edition of the scribe and I hope this helps everybody that reads this to understand trigonometric functions on the Cartisian Plain. Oh yeah the scribe for tomorrow is the one and only... Mel!issa. Have fun and good night y'all!