What is the value of (1000sin(120))/(sin(105)) ?

The value of (1000sin(120))/(sin(105)) is 500(3sqrt(2)-sqrt(6))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(1000sin(120))/(sin(105))

\frac{1000 sin ( 12 0 ^{\circ} )}{sin ( 10 5 ^{\circ} )}

500 (32 - 6)

Solution steps

\frac{1000 sin ( 12 0 ^{\circ} )}{sin ( 10 5 ^{\circ} )}

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

Rewrite using trig identities:

sin (10 5^{\circ}) = \frac{2 ( 3 + 1 )}{4}

= \frac{1000 \cdot \frac{3}{2}}{\frac{2 ( 3 + 1 )}{4}}

Simplify

\frac{1000 \cdot \frac{3}{2}}{\frac{2 ( 3 + 1 )}{4}} : 500 (32 - 6)

= 500 (32 - 6)

cos (\frac{π}{2}) - 1

5 sin (\frac{4 π}{3})

\frac{15 sin ( 6 0 ^{\circ} )}{sin ( 3 0 ^{\circ} )}

\frac{sec ( 11 π )}{6}

tanh (1.4)

What is the value of (1000sin(120))/(sin(105)) ?
The value of (1000sin(120))/(sin(105)) is 500(3sqrt(2)-sqrt(6))