What is the value of sin(pi/3)*2^{1/4} ?

The value of sin(pi/3)*2^{1/4} is (3^{1/2})/(2^{3/4)}

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sin(pi/3)*2^{1/4}

sin (\frac{π}{3}) \cdot 2^{\frac{1}{4}}

\frac{3 ^{\frac{1}{2}}}{2 ^{\frac{3}{4}}}

Decimal Notation

1.02988 \dots

Solution steps

sin (\frac{π}{3}) \cdot 2^{\frac{1}{4}}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

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}

= \frac{3}{2}

= \frac{3}{2} \cdot 2^{\frac{1}{4}}

Simplify

\frac{3}{2} \cdot 2^{\frac{1}{4}} : \frac{3 ^{\frac{1}{2}}}{2 ^{\frac{3}{4}}}

\frac{3}{2} \cdot 2^{\frac{1}{4}}

Multiply fractions:

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

= \frac{3 \cdot 2 ^{\frac{1}{4}}}{2}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{4}}}{2} = \frac{1}{2 ^{1 - \frac{1}{4}}}

= \frac{3 ^{\frac{1}{2}}}{2 ^{1 - \frac{1}{4}}}

Subtract the numbers:

1 - \frac{1}{4} = \frac{3}{4}

= \frac{3 ^{\frac{1}{2}}}{2 ^{\frac{3}{4}}}

= \frac{3 ^{\frac{1}{2}}}{2 ^{\frac{3}{4}}}

tan (\frac{180}{3})

arctan (\frac{16.97}{37.67})

arccos (- 0.17)

sin (92.5 5^{\circ}) 18.53

csc (6 4^{\circ}) \frac{125}{4}

What is the value of sin(pi/3)*2^{1/4} ?
The value of sin(pi/3)*2^{1/4} is (3^{1/2})/(2^{3/4)}