simplify sin(x+210)

Solution

simplify

sin (x + 21 0^{\circ})

- \frac{3}{2} sin (x) - \frac{1}{2} cos (x)

Solution steps

sin (x + 21 0^{\circ})

Rewrite using trig identities

= - \frac{3}{2} sin (x) - \frac{1}{2} cos (x)

sin (x + π) + sin (x - π)

\frac{1}{tan ( \frac{7 π}{2} + x )}

sin (arctan (2 t))

8 t^{2} cos (3 t + 3 0^{\circ})

(cos (2 t - \frac{3 π}{4}))^{2}

What is sin(x+210) ?
The solution to sin(x+210) is -(sqrt(3))/2 sin(x)-1/2 cos(x)