How do you evaluate Sin ((-13pi)/4)?

2 Answers
Ratnaker Mehta
Jul 31, 2016

1/sqrt2.

Explanation:

First, we use sin(-theta)=-sintheta, so,

sin(-13pi/4)=-sin(13pi/4)=-sin(3pi+pi/4).

This shows that, 13pi/4=3pi+pi/4 lies in the Third Quadrant in

which, sin is -ve.

Finally, sin(3pi+pi/4)=-sin(pi/4)=-1/sqrt2.

Hence, sin(-13pi/4)-(-1/sqrt2)=1/sqrt2.

Nghi N.
Jul 31, 2016

sqrt2/2

Explanation:

Trig table of special arcs, unit circle, and property of supplementary arcs -->
sin ((-13pi)/4) = sin (-pi/4 - (12pi)/4) = sin (-pi/4 - 3pi) =
= sin (-pi/4 - pi) = - sin (pi/4 + pi) = - (- sin pi/4) =
= sin (pi/4) = sqrt2/2

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