What is the value of sqrt(1-1/3 sin^2(pi/3)) ?

The value of sqrt(1-1/3 sin^2(pi/3)) is (sqrt(3))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(1-1/3 sin^2(pi/3))

1 - \frac{1}{3} sin^{2} (\frac{π}{3})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

1 - \frac{1}{3} sin^{2} (\frac{π}{3})

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}

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

Simplify

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

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

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

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

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

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

Apply exponent rule:

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

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

(3)^{2} : 3

Apply radical rule:

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

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

Apply exponent rule:

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

= 3^{\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

= 3

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

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

Cross-cancel:

3

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

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

2^{2} = 4

= 1 - \frac{1}{4}

Join

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

1 - \frac{1}{4}

Convert element to fraction:

1 = \frac{1 \cdot 4}{4}

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

Since the denominators are equal, combine the fractions:

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

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

1 \cdot 4 - 1 = 3

1 \cdot 4 - 1

Multiply the numbers:

1 \cdot 4 = 4

= 4 - 1

Subtract the numbers:

4 - 1 = 3

= 3

= \frac{3}{4}

= \frac{3}{4}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{3}{2}

= \frac{3}{2}

\frac{7 sin ( - 0.001 )}{- 0.001}

\frac{cos ( 6 0 ^{\circ} )}{2}

\frac{arctan ( \frac{4}{3} )}{2}

sec (\frac{π}{3}) \cdot tan (\frac{π}{3})

arcsin (\frac{sin ( 4 1 ^{\circ} )}{1.56})

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