What is the value of 1000+100sin((20pi)/(12)) ?

The value of 1000+100sin((20pi)/(12)) is 1000-50sqrt(3)

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1000+100sin((20pi)/(12))

1000 + 100 sin (\frac{20 π}{12})

1000 - 503

Solution steps

1000 + 100 sin (\frac{20 π}{12})

Rewrite using trig identities:

sin (\frac{20 π}{12}) = 2 sin (\frac{5 π}{6}) cos (\frac{5 π}{6})

= 1000 + 100 \cdot 2 sin (\frac{5 π}{6}) cos (\frac{5 π}{6})

Simplify

= 1000 + 200 sin (\frac{5 π}{6}) cos (\frac{5 π}{6})

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

= 1000 + 200 \cdot \frac{1}{2} (- \frac{3}{2})

Simplify

1000 + 200 \cdot \frac{1}{2} (- \frac{3}{2}) : 1000 - 503

= 1000 - 503

\frac{12}{sin ( 4 1 ^{\circ} )}

\frac{270 + 21}{\frac{6}{π} \cdot sin ( \frac{6}{π} ) 2 \cdot cos ( 3 0 ^{\circ} )}

sin (- \frac{3 π}{4}) + cos (- \frac{π}{3})

arctan (\frac{6}{1}) + 180

sin (\frac{π}{2} \cdot 4)

What is the value of 1000+100sin((20pi)/(12)) ?
The value of 1000+100sin((20pi)/(12)) is 1000-50sqrt(3)