Nathan's Blog

For this blog, I will go over a few examples of each section. This week, we basically prepared for the two chapter ten free response tests.

We couldn't use calculators in this whole chapter, and no one liked that.

Section 10-1
Find the exact value of sin15
sin(45-30)=sin45cos30-cos45sin30
=(√2/2)(√3/2)-(√2/2)(1/2)
=√6-√2/4

cos50cos10-sin50sin10
=cos(50+10)
=cos(60)
=1/2

sin5π/12cosπ/12+cos5π/12sinπ/12
=sin(5π/12+π/12)
=sin6/12
=sinπ/2
=1

Section 10-2
This is basically section 10-1 but it involves tan instead of sin and cos.

tan27+tan18/1-tan27tan18
=tan(27+18)
=tan45
=1

tan(x+π/4)=tanx+tanπ/4/1-tanxtanπ/4
=tanx+1/1-tanx

Section 10-3
In this section we used a little bit of chapter 8, in how we simplified the problem, but we used formulas from chapter 10.

2sin10cos10=sin2(10)=sin20
1-2sin^2 35=cos2(35)=cos70
1-sin^2x=cos^2 x
2sin3(alpha)cos3(alpha)=sin2(3 alpha)=sin6(alpha)

Overall, I thought that chapter ten was a semi-hard, semi-easy chapter. There were a ton of formulas that you needed to know. If you knew them, then the chapter was pretty easy,but if you failed to study formulas, then it was a very tough chapter.