What is 2sin(2pi(1/8)+5pix) ?

The solution to 2sin(2pi(1/8)+5pix) is sqrt(2)cos(5pix)+sqrt(2)sin(5pix)

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simplify 2sin(2pi(1/8)+5pix)

simplify

2 sin (2 π (\frac{1}{8}) + 5 π x)

2 cos (5 π x) + 2 sin (5 π x)

Solution steps

2 sin (2 π (\frac{1}{8}) + 5 π x)

Rewrite using trig identities

= 2 \cdot \frac{2 cos ( 5 π x ) + 2 sin ( 5 π x )}{2}

Simplify

2 \cdot \frac{2 cos ( 5 π x ) + 2 sin ( 5 π x )}{2} : 2 cos (5 π x) + 2 sin (5 π x)

= 2 cos (5 π x) + 2 sin (5 π x)

sin (- arcsin (x))

sin^{2} (x + 36 0^{\circ})

sin (x - \frac{4 π}{3})

csc (arcsec (x))

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

What is 2sin(2pi(1/8)+5pix) ?
The solution to 2sin(2pi(1/8)+5pix) is sqrt(2)cos(5pix)+sqrt(2)sin(5pix)