Addition/subtraction formulas for sine or cosine to simplify the following

Jul 2015
707
25
United States
cos(3pi/10)cos(pi/5)-sin(3pi/10)sin(pi/5)

factor cos and sin and get common denominators and combine:

cos(5pi/10)-sin(5pi/10)

cosine(90 degrees)-sin(90 degrees)

0-1

answer is -1? Am I correct?

Wait I see the formula for this is : cos(a+b)

so then I do cos(3pi/10+pi/5)

cos(5pi/10)

and that =0? Is that how I do it?
 
Last edited:

topsquark

Forum Staff
Jan 2006
11,602
3,458
Wellsville, NY
cos(3pi/10)cos(pi/5)-sin(3pi/10)sin(pi/5)

factor cos and sin and get common denominators and combine:

cos(5pi/10)-sin(5pi/10)

cosine(90 degrees)-sin(90 degrees)

0-1

answer is -1? Am I correct?

Wait I see the formula for this is : cos(a+b)

so then I do cos(3pi/10+pi/5)

cos(5pi/10)

and that =0? Is that how I do it?
Your second method is correct.

-Dan
 
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Debsta

MHF Helper
Oct 2009
1,363
635
Brisbane
cos(3pi/10)cos(pi/5)-sin(3pi/10)sin(pi/5)

factor cos and sin and get common denominators and combine:

cos(5pi/10)-sin(5pi/10) No No No

cosine(90 degrees)-sin(90 degrees)

0-1

answer is -1? Am I correct? No

Wait I see the formula for this is : cos(a+b) Yes Yes Yes Stick to the rules!

so then I do cos(3pi/10+pi/5)

cos(5pi/10)

and that =0? Is that how I do it? Yes
Stick to the rules.
 
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skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
cos(3pi/10)cos(pi/5)-sin(3pi/10)sin(pi/5)
$\cos\left(\dfrac{3\pi}{10}\right)\cos\left(\dfrac{2\pi}{10}\right) - \sin\left(\dfrac{3\pi}{10}\right)\sin\left(\dfrac{2\pi}{10}\right) \ne \cos\left(\dfrac{5\pi}{10}\right) - \sin\left(\dfrac{5\pi}{10}\right)$

the identity is ...

$\cos{a}\cos{b} - \sin{a}\sin{b} = \cos(a+b)$


$\cos\left(\dfrac{3\pi}{10}\right)\cos\left(\dfrac{2\pi}{10}\right) - \sin\left(\dfrac{3\pi}{10}\right)\sin\left(\dfrac{2\pi}{10}\right) = \cos\left(\dfrac{3\pi}{10} + \dfrac{2\pi}{10}\right) = \cos\left(\dfrac{\pi}{2}\right) = 0$
 
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