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Solving for a variable inside a sin() 
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#1
Apr406, 10:34 PM

P: 24

sin( degtorad( (180  (180  360/x))/2 ) ) = y/z
degtorad(degrees) means the the degrees inside the parenthesis are converted to radians. How do you solve for x? Thank you. 


#2
Apr406, 11:08 PM

P: 214

you can eliminate the 180's by using properties of sine
sin (180+ x) = sin x = sin(x) also, sin(90+x) = cos(x) 


#3
Apr406, 11:39 PM

P: 24

sin( degtorad( (180  (180  360/x))/2 ) ) = y/z
Is this right? sin( (180  (180  360/x))/2 ) = sin( ( (180  360/x))/2 ) = sin( (180  360/x) /2 ) sin( (180  360/x) /2 ) = sin( ( 360/x) /2 ) = sin( ( 180/x) ) = sin( 180/x ) sin( 180/x ) = y/z um, then what? 


#4
Apr406, 11:43 PM

P: 214

Solving for a variable inside a sin()
sin( (180  360/x) /2 ) = sin (90  180/x) = cos(180/x) = cos (180/x)
Are you familiar with arccos (or cos^{1})? By the way, what exactly are y and z? 


#5
Apr506, 06:03 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,310

Shorn of all the other things, arcsin( ) (also written sin^{1}( )) is defined as the inverse of sin( ) and arccos() (also written cos^{1}( )) is defined as the inverse of cos( ) (well, principal value). That is, arcsin(sin(x))= x and arccos(cos(x))= x.
You have to be a bit careful about that: since sin(x) and cos(x) are not "onetoone" they don't have inverses, strictly speaking. Given an x between 1 and 1, there exist an infinite number of y such that sin(y)= x or cos(y)= x. Arcsin(x) always gives the value, y, between pi/2 and pi/2 such that sin(y)= x and arccos(x) always gives the value, y, between 0 and pi such that cos(y)= x. 


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