What is the value of (sin^2(pi/4))/(tan^3(pi/4)) ?

The value of (sin^2(pi/4))/(tan^3(pi/4)) is 1/2

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(sin^2(pi/4))/(tan^3(pi/4))

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

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{2}{2}

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= \frac{( \frac{2}{2} ) ^{2}}{1 ^{3}}

Simplify

\frac{( \frac{2}{2} ) ^{2}}{1 ^{3}} : \frac{1}{2}

\frac{( \frac{2}{2} ) ^{2}}{1 ^{3}}

Apply rule

1^{a} = 1

1^{3} = 1

= \frac{( \frac{2}{2} ) ^{2}}{1}

(\frac{2}{2})^{2} = \frac{1}{2}

(\frac{2}{2})^{2}

Apply exponent rule:

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

= \frac{( 2 ) ^{2}}{2 ^{2}}

(2)^{2} : 2

Apply radical rule:

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

= (2^{\frac{1}{2}})^{2}

Apply exponent rule:

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

= 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

= 2

= \frac{2}{2 ^{2}}

Cancel the common factor:

2

= \frac{1}{2}

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

Apply the fraction rule:

\frac{a}{1} = a

= \frac{1}{2}

= \frac{1}{2}

arcsin (1) - arcsin (- \frac{1}{2})

arctan (\frac{3}{25})

2 sec (0) tan (0)

\frac{csc ( π )}{6}

1.5 (2 - cos (12 0^{\circ}))

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