What is the value of (sin(3 pi/2))/3 ?

The value of (sin(3 pi/2))/3 is (sin((3pi)/2))/(3)

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(sin(3 pi/2))/3

\frac{sin ( 3 \frac{π}{2} )}{3}

\frac{sin ( \frac{3 π}{2} )}{3}

Decimal Notation

- 0.33333 \dots

Solution steps

\frac{sin ( 3 \cdot \frac{π}{2} )}{3}

Rewrite as

= sin (2 \cdot \frac{3 π}{4})

Rewrite using trig identities:

sin (2 \cdot \frac{3 π}{4}) = 2 sin (\frac{3 π}{4}) cos (\frac{3 π}{4})

sin (2 \cdot \frac{3 π}{4})

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (\frac{3 π}{4}) cos (\frac{3 π}{4})

= \frac{sin ( 3 \cdot \frac{π}{2} )}{3}

Simplify:

3 \cdot \frac{π}{2} = \frac{3 π}{2}

3 \cdot \frac{π}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 3}{2}

= \frac{sin ( \frac{3 π}{2} )}{3}

350 cos (5 0^{\circ})

cos (1 + π)

arctan (4) + π

arctan (- 0.6)

1.342 \cdot sin (8)

What is the value of (sin(3 pi/2))/3 ?
The value of (sin(3 pi/2))/3 is (sin((3pi)/2))/(3)