What is the value of 8.5cos((2pi)/3 (2.5-1.3))-35.5 ?

The value of 8.5cos((2pi)/3 (2.5-1.3))-35.5 is (-17sqrt(5)-301)/8

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8.5cos((2pi)/3 (2.5-1.3))-35.5

8.5 cos (\frac{2 π}{3} (2.5 - 1.3)) - 35.5

\frac{- 17 5 - 301}{8}

Solution steps

8.5 cos (\frac{2 π}{3} (2.5 - 1.3)) - 35.5

= \frac{17}{2} cos (\frac{2 π}{3} (\frac{5}{2} - \frac{13}{10})) - \frac{71}{2}

Simplify:

\frac{2 π}{3} (\frac{5}{2} - \frac{13}{10}) = \frac{4 π}{5}

\frac{17}{2} cos (\frac{4 π}{5}) - \frac{71}{2} = \frac{17 cos ( \frac{4 π}{5} ) - 71}{2}

= \frac{17 cos ( \frac{4 π}{5} ) - 71}{2}

Rewrite using trig identities:

cos (\frac{4 π}{5}) = - \frac{5 + 1}{4}

= \frac{17 ( - \frac{5 + 1}{4} ) - 71}{2}

Simplify

\frac{17 ( - \frac{5 + 1}{4} ) - 71}{2} : \frac{- 17 5 - 301}{8}

= \frac{- 17 5 - 301}{8}

arccot (2.11621)

cos^{4} (4)

arcsin (\frac{1}{1.51})

arctan (\frac{4}{- 5})

\frac{sin ( 3 5 ^{\circ} )}{sin ( 3 0 ^{\circ} )}

What is the value of 8.5cos((2pi)/3 (2.5-1.3))-35.5 ?
The value of 8.5cos((2pi)/3 (2.5-1.3))-35.5 is (-17sqrt(5)-301)/8