# sin (180 - c) = sin c how ?

• Apr 1st 2011, 06:51 AM
saha.subham
sin (180 - c) = sin c how ?
i was going through an example in my book and cam across a step
a + b + c = 180
a+ b+ = 180 - c
sin ( a + b) = sin (180 - c) = sin c

i am not being able to understand how
sin (180 - c) = sin c
• Apr 1st 2011, 06:56 AM
Quacky
No, it isn't a printing mistake. The sin curve is periodic and fluctuates between -1 and 1 every 360 degrees, causing oscillations which can be divided into symmetrical sections.

See the graph of y=sin(x) here
• Apr 1st 2011, 07:00 AM
skeeter
Quote:

Originally Posted by saha.subham
i was going through an example in my book and cam across a step
a + b + c = 180
a+ b+ = 180 - c
sin ( a + b) = sin (180 - c) = sin c

i am not being able to understand how
sin (180 - c) = sin c

$\displaystyle \sin(180-c) = \sin(180)\cos(c) - \cos(180)\sin(c) = (0) \cdot \cos(c) - (-1) \cdot \sin(c) = \sin(c)$
• Apr 1st 2011, 07:00 AM
topsquark
Quote:

Originally Posted by saha.subham
i was going through an example in my book and cam across a step
a + b + c = 180
a+ b+ = 180 - c
sin ( a + b) = sin (180 - c) = sin c

i am not being able to understand how
sin (180 - c) = sin c

Another way:
$\displaystyle sin(a - b) = sin(a)~cos(b) - sin(b)~cos(a)$

$\displaystyle sin(180 - c) = sin(180)~cos(c) - sin(c)~cos(180)$
$\displaystyle = (0)~cos(c) - sin(c)~(-1) = 0 - (-sin(c)) = sin(c)$