What is the value of 7cos(3.8pi) ?

The value of 7cos(3.8pi) is (7(sqrt(5)+1))/4

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7cos(3.8pi)

7 cos (3.8 π)

\frac{7 ( 5 + 1 )}{4}

Solution steps

7 cos (3.8 π)

= 7 cos (\frac{19}{5} π)

Simplify:

\frac{19}{5} π = \frac{19 π}{5}

= 7 cos (\frac{19 π}{5})

cos (\frac{19 π}{5}) = cos (\frac{9 π}{5})

= 7 cos (\frac{9 π}{5})

Rewrite using trig identities:

cos (\frac{9 π}{5}) = cos (\frac{π}{5})

= 7 cos (\frac{π}{5})

Rewrite using trig identities:

cos (\frac{π}{5}) = \frac{5 + 1}{4}

= 7 \cdot \frac{5 + 1}{4}

Simplify

7 \cdot \frac{5 + 1}{4} : \frac{7 ( 5 + 1 )}{4}

= \frac{7 ( 5 + 1 )}{4}

sin (\frac{13}{12})

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arctan (0.0875)

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