What is the value of 1/2 sin(3((5pi)/6)-pi) ?

The value of 1/2 sin(3((5pi)/6)-pi) is (sin((3pi)/2))/(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1/2 sin(3((5pi)/6)-pi)

\frac{1}{2} sin (3 (\frac{5 π}{6}) - π)

\frac{sin ( \frac{3 π}{2} )}{2}

Decimal Notation

- 0.5

Solution steps

\frac{1}{2} sin (3 (\frac{5 π}{6}) - π)

= \frac{1}{2} sin (3 \cdot \frac{5 π}{6} - π)

Rewrite as

= sin (2 \cdot \frac{3 π}{4})

Rewrite using trig identities:

sin (2 \cdot \frac{3 π}{4}) = 2 sin (\frac{3 π}{4}) cos (\frac{3 π}{4})

sin (2 \cdot \frac{3 π}{4})

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (\frac{3 π}{4}) cos (\frac{3 π}{4})

= \frac{1}{2} sin (3 \cdot \frac{5 π}{6} - π)

Simplify:

3 \cdot \frac{5 π}{6} - π = \frac{3 π}{2}

3 \cdot \frac{5 π}{6} - π

3 \cdot \frac{5 π}{6} = \frac{5 π}{2}

3 \cdot \frac{5 π}{6}

Multiply fractions:

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

= \frac{5 π 3}{6}

Multiply the numbers:

5 \cdot 3 = 15

= \frac{15 π}{6}

Cancel the common factor:

3

= \frac{5 π}{2}

= \frac{5 π}{2} - π

Convert element to fraction:

π = \frac{π 2}{2}

= \frac{5 π}{2} - \frac{π 2}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{5 π - π 2}{2}

Add similar elements:

5 π - 2 π = 3 π

= \frac{3 π}{2}

\frac{1}{2} sin (\frac{3 π}{2}) = \frac{sin ( \frac{3 π}{2} )}{2}

\frac{1}{2} sin (\frac{3 π}{2})

Multiply fractions:

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

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

Multiply:

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

= \frac{sin ( \frac{3 π}{2} )}{2}

= \frac{sin ( \frac{3 π}{2} )}{2}

cos (74. 5^{\circ})

π \cdot cos (\frac{π}{4})

sin (- \frac{14 π}{3})

\frac{1 + cos ( \frac{5}{13} )}{2}

sin (\frac{6 π}{7}) cos (\frac{11 π}{21}) - cos (\frac{6 π}{7}) sin (\frac{11 π}{21})

What is the value of 1/2 sin(3((5pi)/6)-pi) ?
The value of 1/2 sin(3((5pi)/6)-pi) is (sin((3pi)/2))/(2)