What is the value of -sin((sqrt(pi/2))^2)*2(sqrt(pi/2)) ?

The value of -sin((sqrt(pi/2))^2)*2(sqrt(pi/2)) is -sqrt(2)sqrt(pi)

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-sin((sqrt(pi/2))^2)*2(sqrt(pi/2))

- sin ((\frac{π}{2})^{2}) \cdot 2 (\frac{π}{2})

- 2 π

Decimal Notation

- 2.50662 \dots

Solution steps

- sin ((\frac{π}{2})^{2}) \cdot 2 (\frac{π}{2})

= - sin ((\frac{π}{2})^{2}) \cdot 2 \frac{π}{2}

Rewrite using trig identities:

sin ((\frac{π}{2})^{2}) = 1

sin ((\frac{π}{2})^{2})

Simplify:

(\frac{π}{2})^{2} = \frac{π}{2}

(\frac{π}{2})^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

= ((\frac{π}{2})^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (\frac{π}{2})^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

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

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= \frac{π}{2}

= sin (\frac{π}{2})

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

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}

= 1

= 1

= - 1 \cdot 2 \frac{π}{2}

Simplify

- 1 \cdot 2 \frac{π}{2} : - 2 π

- 1 \cdot 2 \frac{π}{2}

Apply exponent rule:

a \frac{b}{a} = a^{2} \frac{b}{a}

2 \frac{π}{2} = 2^{2} \cdot \frac{π}{2}

= - 1 \cdot 2^{2} \cdot \frac{π}{2}

Multiply:

1 \cdot 2^{2} \cdot \frac{π}{2} = 2^{2} \cdot \frac{π}{2}

= - 2^{2} \cdot \frac{π}{2}

Multiply

2^{2} \cdot \frac{π}{2} : 2 π

2^{2} \cdot \frac{π}{2}

Multiply fractions:

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

= \frac{π 2 ^{2}}{2}

Cancel the common factor:

2

= 2 π

= - 2 π

Apply radical rule:

assuming

a \geq 0, b \geq 0

= - 2 π

= - 2 π

\frac{( 2 \cdot 5 \cdot 4 π \cdot cos ^{2} ( 4 π \cdot 0.3 ) )}{1000}

arcsin (\frac{14.1}{49.5})

2 (1) + cos (1)

arctan (17)

cos (3 0^{\circ} + 12 0^{\circ})

What is the value of -sin((sqrt(pi/2))^2)*2(sqrt(pi/2)) ?
The value of -sin((sqrt(pi/2))^2)*2(sqrt(pi/2)) is -sqrt(2)sqrt(pi)