Thread: 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
can anyone please help me?? is it a printing mistake?? thanks in advance

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

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
can anyone please help me?? is it a printing mistake?? thanks in advance

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
can anyone please help me?? is it a printing mistake?? thanks in advance

Another way:


In your case




-Dam

Or- using the "circular definition" of sine, sin(t) is the y coordinate of the point (x, y) an angle t, measured counter-clockwise from the positive x-axis. along the circumference of the unit circle. sin(180- x) would be measured back, clockwise from the negative x-axis. By the symmetry of the circle, those two points have the same y value (and their x coordinates have opposite sign- cos(180- c)= -cos(c)).

does a sketch help?