February 22

Today in class we discussed the visual location of the tangent, sine, cosine, and cosecant on the unit circle. We played around with this idea using Geogebra and Mr. O'Brien drew up some notes on the board. Here's a nice visual I found online:



Next, we went over the second unit four homework quiz. Mr. O'Brien reminded us to make sure our calculators are in the correct unit (degrees/radians) when you answer a problem.

Some other concepts we reviewed were converting angle measurements to decimal degree form (and vice versa). Here are some examples:

Decimal Degree Form to Angle Measure:
87˚ 18' 30"
87 + 18/60 + 30/3600
= 87.308

Angle Measure to Decimal Degree:
-2.58˚ (times .58 x 60)
= -2˚ + 34.8 (times .8 x 60)
=-2˚ + 34' + 48"
=-2˚ 34' 48"

Mr. OB also said that a helpful formula to remember is that the Area of a Sector = , which was especially useful in solving problem 4.

The remaining time left in class was spent working on new HW:
* p. 318/1, 3, 7, 13, 15, 19, 21, 23, 27, 41, 53, 61, 81, 83, 89, 91
*Read the last two pages of the six page notes handout to learn where the sine function gets its name.
*Have a think about the quarter project
*Keep working on your memorization of the common radian-degree conversion and the 198 trig values

I noticed that the trigonometric identities never made it up onto the blog, so I snagged Kayla's from the Red day class in case anyone needed them.

Identities:
Reciprocal: sinθ=1/cscθ cscθ=1/sinθ
cos θ=1/secθ secθ=1/cosθ
tanθ=1/cotθ cotθ=1/tanθ

Quotient: tanθ=sinθ/cosθ
cotθ= cosθ/sinθ

Co-Function: sinθ=cos((π/2)-θ)
cosθ=sin((π/2)-θ)
secθ=csc((π/2)-θ)
cscθ=sec((π/2)-θ)
tanθ=cot((π/2)-θ)
cotθ=tan((π/2)-θ)

Pythagorean: sin²θ+cos²θ=1 then divide both sides by a sin²θ
which makes it: 1+cot²θ=csc²θ
and also: 1+tan²θ=sec²θ

Remember that there's a homework quiz on Friday! The scribe for next class is Petra.