What is the value of 15sin(2pi*15)+90 ?

The value of 15sin(2pi*15)+90 is 90

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15sin(2pi*15)+90

15 sin (2 π \cdot 15) + 90

90

Solution steps

15 sin (2 π 15) + 90

Simplify

= 15 sin (30 π) + 90

sin (30 π) = sin (0)

sin (30 π)

Rewrite

30 π

2 π \cdot 15 + 0

= sin (2 π 15 + 0)

Apply the periodicity of

sin

sin (x + 2 π \cdot k) = sin (x)

sin (2 π \cdot 15 + 0) = sin (0)

= sin (0)

= 15 sin (0) + 90

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

= 15 \cdot 0 + 90

Simplify

= 90