What is 2sin(3x+pi/6) ?

The solution to 2sin(3x+pi/6) is sqrt(3)sin(3x)+cos(3x)

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simplify 2sin(3x+pi/6)

simplify

2 sin (3 x + \frac{π}{6})

3 sin (3 x) + cos (3 x)

Solution steps

2 sin (3 x + \frac{π}{6})

Rewrite using trig identities

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

Simplify

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

= 3 sin (3 x) + cos (3 x)

cos (9 0^{\circ} - a)

- 9 sin (- x)

2 sin (3 0^{\circ} - x) + cos (x)

sin (2 x - π)

sec (arccsc (\frac{x}{4}))