This class was supposed to be spent to do our unit test on Transformations instead,
Friday Class (Morning)
In this class we started our new unit called Trigonometric Identities.
In this slide it refreshes our memories about the basic trigonometric identities namely the tangent, cosine , and sine and the reciprocal functions namely, secant cosecant and cotangent. Every trigonometric identity is build up of sine and cosine functions. Slide 2
In this slide we practice how to simplify trigonometric expressions into either cosine or sine.For the first example, sine cannot be simplify as anything because it is one of the basic blocks of trigonometric functions, secant can be simplify as 1/cosine , and cotangent can be simplify as cosine/sine. Then you can see that we just simplify everything.Remember that every question in this unit can be answer in different ways. It is just all about algebraic massage. For the second example, cosine cannot be simplified because it is one of the basic blocks, and cosecant can be simplify as 1/sin. Then we just simplifies everything as cos/sin or cotangent. For the third example you can notice that it is a difference of squares so just factor out the secant, as you can see there are three boxed answers because as I said before it can be solve in many different ways by just respecting the right algebra.Slide 3-7
We just continue to simplify everything into either cosine, sine, or 1 but now with more complicated problems.
From the third question in slide 3 Grey-M said that cos^2 +sin^2 =1 which can will proven in the next slide.
Why is cos^2 +sin^2=1? It is because in the unit circle the distance of the x-axis is the cosine , the distance of the y-axis is the sine the radius is 1 and all the triangles are right angle so by the phytagorean theorem sin^2 +cos^2 must always equals 1 from this we generate the phytagorean identity.Slide 10
In this slide we got all the corollaries by just algebraically massaging the pythagorean identity.Friday (Afternoon)
This class was spent to write our test on Transformations.
Thats it for my scribe. The next scribe is MilesM. Pie day is just two days away!!!!!!