My Math Forum adding subtracting multiples of 360

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 November 27th, 2016, 09:39 AM #1 Member   Joined: Nov 2016 From: Ireland Posts: 64 Thanks: 2 adding subtracting multiples of 360 Hi folks I'm doing some study into adding subtracting multiples of 360. Something's confusing me - probably really easy but I can't figure it. Ok in one question it asks: Simplify the sin (x + 400) = sin (x+40) Yet sin (Î¸ + 1000) = sin (Î¸ - 80) Why is the second one not equal to Sin (Î¸ + 280)? Last edited by skipjack; November 27th, 2016 at 11:44 AM.
 November 27th, 2016, 09:50 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,287 Thanks: 1119 $\sin(\theta+1000^\circ) = \sin{\theta}\cos(1000^\circ) + \cos{\theta}\sin(1000^\circ) = \sin{\theta}\cos(-80^\circ) + \cos{\theta}\sin(-80^\circ) = \sin{\theta}\cos(80^\circ) - \cos{\theta}\sin(80^\circ) = \sin(\theta - 80^\circ)$ Thanks from Kevineamon Last edited by skeeter; November 27th, 2016 at 10:05 AM.
 November 27th, 2016, 09:54 AM #3 Member   Joined: Nov 2016 From: Ireland Posts: 64 Thanks: 2 Ok I'm a n00b that's even more confusing lol. I've noticed the answers are all <180. Most are <90 degrees.
 November 27th, 2016, 10:12 AM #4 Math Team   Joined: Jul 2011 From: Texas Posts: 2,287 Thanks: 1119 you need to learn some identities, namely ... sum/difference identities for sine & cosine $\sin(a \pm b) = \sin{a}\cos{b} \pm \cos{a}\sin{b}$ $\cos(a \pm b) = \cos{a}\cos{b} \mp \sin{a}\sin{b}$ odd/even identities for sine & cosine ... $\sin(-\theta) = -\sin{\theta}$ $\cos(-\theta) = \cos{\theta}$
 November 27th, 2016, 10:27 AM #5 Math Team   Joined: Jul 2011 From: Texas Posts: 2,287 Thanks: 1119 I may have made it more difficult than necessary ... note that $1000 - 3(360) = -80$ Thanks from Kevineamon
 November 27th, 2016, 10:34 AM #6 Member   Joined: Nov 2016 From: Ireland Posts: 64 Thanks: 2 Ok thanks Skeeter I'll struggle on through it. I'm liking the odds of the answer being less than 180 degrees. I shall invent a new mathematical law. No proof necessary
 November 28th, 2016, 11:13 AM #7 Newbie   Joined: Nov 2016 From: Canada Posts: 13 Thanks: 3 Math Focus: All sin(n*360 + x) = sin x.

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