If Sin(A)=Sin(B), then does that mean that A=B?

Question

This is a rule that I came across in a textbook, this got me thinking, that Sin(180)=Sin(360) so does that mean that 180=360? Obviously not, but is this a contradiction of that rule or am I missing something? Thanks in advance guys.

lenpol7 · Answer

Trigs are 'FUNCTIONS'. 
That means you can put in several different values to get the same o
answer out.

Sin 0 = 0 
Sin180 = 0 
Sin 360 = 0 
et.seq.

Similarly 
Cos 0 = 1 
Cos 360 = 1 
Careful with this one because the Cos & Sin functions are complementary . 
Cos 180 = -1

Similarly 
Tan 0 = 0 
Tan 180 = 0 
Tan 360 = 0

et.seq.

With all mathematical 'FUNCTIONS' you can put in several different values and get the same result.

The Sine/Cosine function(s) are waves that repeat every 360 degrees. 
The Tangent function repeats every 180 degrees.

xyzzy · Answer

not necessarily

if A = B then sin A = sin B
but it doesn't go the other way.

sin pi/4 = sin 3pi/4 = sin 9pi/4 .....
we could say that the sin function is not one to one.

Anonymous · Answer

Technically speaking, sin180 = sin360, because their value are both zero. However, the two positions in a coordinated circle have opposite places. Sin180 is located at the negative side of the x-axis, while sin360 is located at the positive side of the x-axis, and they have different cosine values.

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If Sin(A)=Sin(B), then does that mean that A=B?

3 Answers