What is the value of 0.8*4/(2pi)cos((2pi)/4*1.5+pi/2) ?

The value of 0.8*4/(2pi)cos((2pi)/4*1.5+pi/2) is -(4sqrt(2))/(5pi)

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0.84/(2pi)cos((2pi)/41.5+pi/2)

0.8 \cdot \frac{4}{2 π} cos (\frac{2 π}{4} \cdot 1.5 + \frac{π}{2})

- \frac{4 2}{5 π}

Solution steps

0.8 \cdot \frac{4}{2 π} cos (\frac{2 π}{4} \cdot 1.5 + \frac{π}{2})

= \frac{4}{5} \cdot \frac{4}{2 π} cos (\frac{2 π}{4} \cdot \frac{3}{2} + \frac{π}{2})

Rewrite using trig identities:

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

= \frac{4}{5} \cdot \frac{4}{2 π} (cos (\frac{3 π}{4}) cos (\frac{π}{2}) - sin (\frac{3 π}{4}) sin (\frac{π}{2}))

\frac{4}{5} \cdot \frac{4}{2 π} (cos (\frac{3 π}{4}) cos (\frac{π}{2}) - sin (\frac{3 π}{4}) sin (\frac{π}{2})) = \frac{8 ( cos ( \frac{π}{2} ) cos ( \frac{3 π}{4} ) - sin ( \frac{π}{2} ) sin ( \frac{3 π}{4} ) )}{5 π}

= \frac{8 ( cos ( \frac{π}{2} ) cos ( \frac{3 π}{4} ) - sin ( \frac{π}{2} ) sin ( \frac{3 π}{4} ) )}{5 π}

Use the following trivial identity:

cos (\frac{π}{2}) = 0

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{2}) = 1

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

= \frac{8 ( 0 \cdot ( - \frac{2}{2} ) - 1 \cdot \frac{2}{2} )}{5 π}

Simplify

\frac{8 ( 0 \cdot ( - \frac{2}{2} ) - 1 \cdot \frac{2}{2} )}{5 π} : - \frac{4 2}{5 π}

= - \frac{4 2}{5 π}

7 + sec^{2} (0)

3^{c o s (5 + 5)} + 1

1 - cos^{2} (\frac{9 π}{8})

tan (arccos (\frac{12}{20}))

sec^{2} (- 0.01)

What is the value of 0.8*4/(2pi)cos((2pi)/4*1.5+pi/2) ?
The value of 0.8*4/(2pi)cos((2pi)/4*1.5+pi/2) is -(4sqrt(2))/(5pi)