What is the value of 2(pi/4)+sin(4(pi/4)) ?

The value of 2(pi/4)+sin(4(pi/4)) is pi/2

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2(pi/4)+sin(4(pi/4))

2 (\frac{π}{4}) + sin (4 (\frac{π}{4}))

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

2 (\frac{π}{4}) + sin (4 (\frac{π}{4}))

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

Rewrite using trig identities:

sin (4 \cdot \frac{π}{4}) = 0

sin (4 \cdot \frac{π}{4})

Simplify:

4 \cdot \frac{π}{4} = π

4 \cdot \frac{π}{4}

Multiply fractions:

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

= \frac{π 4}{4}

Cancel the common factor:

4

= π

= sin (π)

Use the following trivial identity:

sin (π) = 0

sin (π)

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

= 0

= 2 \cdot \frac{π}{4} + 0

Simplify

2 \cdot \frac{π}{4} + 0 : \frac{π}{2}

2 \cdot \frac{π}{4} + 0

2 \cdot \frac{π}{4} = \frac{π}{2}

2 \cdot \frac{π}{4}

Multiply fractions:

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

= \frac{π 2}{4}

Cancel the common factor:

2

= \frac{π}{2}

= \frac{π}{2} + 0

\frac{π}{2} + 0 = \frac{π}{2}

= \frac{π}{2}

= \frac{π}{2}

sec (36.8 7^{\circ})

\frac{5 ( 9.81 ) sin ( 3 7 ^{\circ} ) + 20}{5}

csc (arccos (- \frac{4}{7}))

arcsin (\frac{39}{62})

tan (\frac{5}{5 3})

What is the value of 2(pi/4)+sin(4(pi/4)) ?
The value of 2(pi/4)+sin(4(pi/4)) is pi/2