Question

Why does sin(pi-x)=sin(x)? Where x is angle measure in radians.

Answer 1

\[\sin (\pi-\theta)=\sin \theta \]

Answer 2

If I remember correctly \(sin(\pi - \theta) = -sin\theta\).

To verify this identity we can use our beloved Addition Identity: \(sin(A - B) = sinAcosB - cosAsinB\).
Substitute 360 degrees and theta in, we have
\(sin(360)cos\theta - cos(360)sin(\theta)\)
\(= 0 cos\theta - (1) sin\theta\)
\(= -sin\theta\)

Answer 3

radians not degrees right?

Answer 4

if you convert, which you should not, you would use 180 degrees instead of 360

Answer 5

@satellite73 If didn't memorize the radians to degrees chart wrong, \(\pi / 2 = 180\), which would make \(\pi = 360\).

Answer 6

a complete rotation is 360 degrees, which in radians is \(2\pi\)
a straight angle is \(\pi\) or in degrees 180
a right angle is \(\frac{\pi}{2}\) or in degrees 90

Answer 7

@satellite73 I see (never used radians in my maths curriculum so I like conversion better)

So back to the drawing board:
\(sin(A - B) = sinAcosB - cosAsinB\)
Substitute 180 - theta into this equation, we have
\(sin180cos\theta - cos180sin\theta\)
\(= 0 cos\theta - (-1) sin\theta\)
\(= sin(\theta)\)

Answer 8

the answer is sin x according to my textbook and teacher

Answer 9

Can you describe why in terms of a unit circle. I don't really understand your proof

Answer 10

sin(A−B)=sinAcosB−cosAsinB that part

Answer 11

I don't have my textbook on hand so I'll try my best at explaining why sin(180 - x) = sin(x). For the addition formula, the complete proof is pretty hard to understand (but if you want to try your luck, it's here: http://en.wikipedia.org/wiki/Proofs_of_trigonometric_identities ), so your best bet is to memorize it for now.

(Proof below - need access to my graph)

Answer 12

As you can see, the formation of theta in quadrant I is simply mirrored over to form 180 - theta over at quadrant II.

(Somebody probably can explain better than me)