What is the value of 5/3 (4pi+3)sin((4pi)/3) ?

The value of 5/3 (4pi+3)sin((4pi)/3) is -(5sqrt(3)(4pi+3))/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

5/3 (4pi+3)sin((4pi)/3)

\frac{5}{3} (4 π + 3) sin (\frac{4 π}{3})

- \frac{5 3 ( 4 π + 3 )}{6}

Solution steps

\frac{5}{3} (4 π + 3) sin (\frac{4 π}{3})

Rewrite using trig identities:

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

= \frac{5}{3} (4 π + 3) \cdot 2 sin (\frac{2 π}{3}) cos (\frac{2 π}{3})

\frac{5}{3} (4 π + 3) \cdot 2 sin (\frac{2 π}{3}) cos (\frac{2 π}{3}) = \frac{10 sin ( \frac{2 π}{3} ) cos ( \frac{2 π}{3} ) ( 4 π + 3 )}{3}

= \frac{10 sin ( \frac{2 π}{3} ) cos ( \frac{2 π}{3} ) ( 4 π + 3 )}{3}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

= \frac{10 \cdot \frac{3}{2} ( - \frac{1}{2} ) ( 4 π + 3 )}{3}

Simplify

\frac{10 \cdot \frac{3}{2} ( - \frac{1}{2} ) ( 4 π + 3 )}{3} : - \frac{5 3 ( 4 π + 3 )}{6}

= - \frac{5 3 ( 4 π + 3 )}{6}

4 sin^{2} (40 0^{\circ})

cos (240 0^{\circ})

tan (\frac{8}{10})

(sin (0))^{2}

2 cos^{2} (3 0^{\circ}) + 3 sin^{2} (3 0^{\circ})

What is the value of 5/3 (4pi+3)sin((4pi)/3) ?
The value of 5/3 (4pi+3)sin((4pi)/3) is -(5sqrt(3)(4pi+3))/6