Question

sin(3pi+x)=?

Answer 1

\[\sin(3\pi+x)=-sinx\]

Answer 2

how

Answer 3

it lies in third quadrant so sin is negative

Answer 4

for more info: http://www.wolframalpha.com/input/?i=sin%283pi%2Bx%29%3D&dataset=

Answer 5

Can also use double angle

Sin(3pi+x) = Sin3piCosx + Cos3piSinx = -sinx

Answer 6

If you want it in degrees, then\[\rm \sin(3\pi + x) = \sin(180^{\circ} + x)\]

Answer 7

We know that \(\rm \sin(x) = \sin(360^{\circ} + x)\) so we are actually \(180^{\circ}\) behind. This provides good insight.