Welcome to our classroom blog...

Welcome to the grade 12 precalculus math blog of St.James Collegiate....

Thursday, February 24, 2011

Wednesday, February 16, 2011

Checking in on Circular Functions

Well we are progressing nicely through the Circular Functions Unit.  Students are getting very comfortable with the radian measures on the unit circle and have now moved on to learning exact values/coordinates.  Students have come to the understanding that once they know the exact values in quadrant one of the coordinate plane, all they need to be able to do is reflect these coordinates into the other four quadrants, while being mindful of the negative x in quadrants 2 and 3, and the negative y in quadrant 3 and 4. 

In Lesson 4 we looked at solving trig equations.  We needed to step back to revisit all of our factoring skills from grade 11 precalculus.  We talked about the ways to factor: factor by gcf, factoring a basic trinomial, factoring a difference of squares and factoring by grouping.  Students are withdrawing this previous knowledge in order to transfer these skills to solving trig equations.  The CAST rule is very useful for this lesson as students need to identify the correct quadrants in which the solution can be found based on the sign of the trigonometric ratio. 

We will be having a quiz on Thursday Feb 17th - the quiz is used "for" learning - as a formative assessment.  To help students understand what they know, and what they need to work on.   For the quiz, students will need to be able to convert from degrees to radians and vice versa as well as identify exact values.  They will also need to complete a unit circle with all of the  missing pieces - radians, exact values, and tangent ratios.  Remember the tangent ratio is the value of y/x. 

The first unit test will be coming up soon.  The date will be posted soon.

Thank you!

Thursday, February 10, 2011

Nick's Question...

Today in class we discussed the special triangles and how they relate to the exact values in the unit circle.  We were looking at the isosceles triangle that has base angles of 45 degrees.  For any isosceles triangle having base angles equal to 45 degrees the sine ratio and cosine ratio will always be the same...ie. 1/sqrt 2.  If we transpose a right isosceles triangle into the unit circle, the hypotenuse will be 1 and the length of legs a and b will be the same, namely 1/sqrt 2.  So the opposite side is 1/sqrt 2 and the adjacent side is 1/sqrt 2.  It follows then that the sine ratio of opposite over hypotenuse is 1/sqrt2 / 1 and cosine ratio of adjacent over hypotenuse is 1/sqrt2 / 1.  
So now we know that cosine 45 degrees = 1/sqrt 2 and sine 45 degrees = 1/sqrt2  
Hope this answers Nick's question!

Lesson 1 Circular Functions

Lesson 2 Circular Functions