Chapter 10 Review

Well, I already did a blog for each section of chapter 10 and we did not learn anything new this week, so I am going to do a review blog. Then I will show you a different type of problem.

Formulas:
1. cos (alpha +/- beta) = cos (alpha) cos (beta) -/+ sin (alpha) sin (beta)
2. sin (alpha +/- beta) = sin (alpha) cos (beta) +/- cos (alpha) sin (beta)
3. sin x + sin y = 2 sin ((x + y)/(2) cos ((x-y)/(2)
4. sin x - sin y = 2 cos ((x+y)/(2) sin ((x-y)/(2)
5. cos x + cos y = 2 cos ((x+y)/(2) cos ((x-y)/(2)
6. cos x - cos y = -2 sin ((x+y)/(2) sin ((x-y)/(2)
7. tan (alpha + beta)= ((tan alpha + tan beta)/(1- tan alpha tan beta))
8. tan (alpha – beta)= ((tan alpha – tan beta)/(1+ tan alpha tan beta))
9. sin 2a= (2 sin a) (cos a)
10. cos 2a= (cos^2 a) – (sin^2 a)
11. cos 2a= 1- 2 sin^2 a
12. cos 2a= 2 cos^2 a -1
13. tan 2a= ( 2 tan a) / ( 1- tan^2 a)
14. sin a/2= +/- sq. root of ((1 – cos a) / (2))
15. cos a/2= +/- sq. root of (( 1+ cos a) / (2))
16. tan a/2= +/- sq. root of (( 1- cos a) / ( 1+cos a))
17. tan a/2= +/- (( sin a) / ( 1+ cos a))
18. tan a/2= +/- (( 1- cos a) / (sin a))
(Remember to replace, not plug in)

Example: Simplify 4 sin pi/6 cos pi/6
• 2(2 sin pi/6 cos pi/6)
• 2(sin 2(pi/6))
• 2(sin (pi/3))
• 2(sq. root 3/2)
• Sq. root of 3

-Braxton