Addition Formulas for Sine and Cosines
Favorites|Homepage
Subscriptions | sitemap
HOME > > Addition Formulas for Sine and Cosines

Addition Formulas for Sine and Cosines

[From: ] [author: ] [Date: 12-05-15] [Hit: ]
......
Use addition formulas for sine and cosine to simplify the trig expression.

sin[B + (pi/6)] - sin[B - (pi/6)]

-
sin (a + b) = sin a cos b + cos a sin b
sin (a - b) = sin a cos b - cos a sin b

sin pi/6 = 1/2
cos pi/6 = sqrt(3) / 2

sub in to give:
sin [B + pi/6] = sin B cos pi/6 + cos B sin pi/6 = sqrt(3) / 2 sin B + 1/2 cos B
sin [B - pi/6] = sin B cos pi/6 - cos B sin pi/6 = sqrt(3) / 2 sin B - 1/2 cos B

so sin [B + pi/6] - sin [B - pi/6] = sqrt(3) / 2 sin B + 1/2 cos B - [sqrt(3) / 2 sin B - 1/2 cos B]
= cos B

sin [B + pi/6] - sin [B - pi/6] = sin [B + pi/6] = cos B

-
Oops, typo on the last line -- that last sin [B + pi/6] shouldn't be there...

Report Abuse

1
keywords: Cosines,and,Formulas,Addition,Sine,for,Addition Formulas for Sine and Cosines
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .