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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin^2((pi/3+pi)/2)

sin^{2} (\frac{\frac{π}{3} + π}{2})

\frac{3}{4}

Decimal Notation

0.75

Solution steps

sin^{2} (\frac{\frac{π}{3} + π}{2})

Simplify:

\frac{\frac{π}{3} + π}{2} = \frac{2 π}{3}

\frac{\frac{π}{3} + π}{2}

Join

\frac{π}{3} + π : \frac{4 π}{3}

\frac{π}{3} + π

Convert element to fraction:

π = \frac{π 3}{3}

= \frac{π}{3} + \frac{π 3}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{π + π 3}{3}

Add similar elements:

π + 3 π = 4 π

= \frac{4 π}{3}

= \frac{\frac{4 π}{3}}{2}

Apply the fraction rule:

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

= \frac{4 π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{4 π}{6}

Cancel the common factor:

2

= \frac{2 π}{3}

= sin^{2} (\frac{2 π}{3})

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

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

Simplify

(\frac{3}{2})^{2} : \frac{3}{4}

(\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}}

2^{2} = 4

= \frac{3}{4}

= \frac{3}{4}

20 sin (1 5^{\circ})

2 + 3 cos (0)

arccos (\frac{0.43}{0.82})

5 \cdot tan (2 5^{\circ})

4 (cos (\frac{π}{6}) + i sin (\frac{π}{6}))

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