What is the value of 4sin(pi+pi)+3 ?

The value of 4sin(pi+pi)+3 is 3

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4sin(pi+pi)+3

4 sin (π + π) + 3

3

Solution steps

4 sin (π + π) + 3

Simplify

= 4 sin (2 π) + 3

sin (2 π) = sin (0)

sin (2 π)

Rewrite

2 π

2 π + 0

= sin (2 π + 0)

Apply the periodicity of

sin

sin (x + 2 π) = sin (x)

sin (2 π + 0) = sin (0)

= sin (0)

= 4 sin (0) + 3

Use the following trivial identity:

sin (0) = 0

sin (0)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= 4 \cdot 0 + 3

Simplify

= 3

arcsin (\frac{14 2}{39})

sin (4 0^{\circ}) cos (5 0^{\circ}) + cos (4 0^{\circ}) sin (5 0^{\circ})

cot (\frac{12}{5})

cos^{3} (2)

sec (5 5^{\circ})