Nathan's Blog

In this blog, I will go over section 10-2 which is basically 10-1, but it involves tan instead of sin and cos. It's just two more formulas that we have to memorize, but these are really easy to remember and apply.

tan(a+b)=tan(a)+tan(b)/1-tan(a)tan(b)
tan(a-b)=tan(a)-tan(b)/1+tan(a)tan(b)

cot is the reciprocal
cot(a+b)=1-cot(a)cot(b)/cot(a)+cot(b)

tan(x+π/4)
=tan(x)+tan(π/4)/1-tan(x)tan(π/4)
=tan(x)+1/1-tan(x)

Simplify

tan110-tan50/1+tan110tan50
=tan(110-50)
=tan(60)
=√3

tan27+tan18/1-tan27tan18
=tan(27+18)
=tan(45)
=1

tan140-tan50/1+tan140tan50
=tan(140-50)
=tan(90)
=undefined

Another type of problem you will see is one like this:

Suppose tan(a)=1/3 and tan(b)=1/2, find tan(a+b).
=(1/3)+(1/2)/1-(1/3)(1/2)
=(2/6)+(3/6)/1-(1/6)
=(5/6)/(5/6)
=1

Now, I will go to section 10-3, where we reviewed how to simplify equations using techniques from chapter 10 and chapter 8. Also, in this section, we learned about ten new formulas, which all come into play at some time.

1.)2sin10cos10=sin2(10)=sin20
2.)cos^2 15-sin^2 15=cos2(15)=cos30=√3/2
3.)1-sin^2 35=cos2(35)=cos70
4.)2cos^2 25-1=cos2(25)=cos50
5.)2tan50/1-tan^2 50=tan2(50)=tan100
6.)1-sin^2 x=cos^2 x
7.)2sin3(a)cos3(a)=sin2(3a)=sin6(a)
8.)cos^2 5y-sin^2 5y=cos2(5y)=cos10y

R.I.P. Bradly Gaude, you are greatly missed down here by your family, friends, and all of Riverside.