What is the value of 3.55cos(pi/6*3)+19.15 ?

The value of 3.55cos(pi/6*3)+19.15 is 383/20

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3.55cos(pi/6*3)+19.15

3.55 cos (\frac{π}{6} \cdot 3) + 19.15

\frac{383}{20}

Decimal Notation

19.15

Solution steps

3.55 cos (\frac{π}{6} \cdot 3) + 19.15

= \frac{71}{20} cos (\frac{π}{6} \cdot 3) + \frac{383}{20}

Rewrite using trig identities:

cos (\frac{π}{6} \cdot 3) = 0

cos (\frac{π}{6} \cdot 3)

Simplify:

\frac{π}{6} \cdot 3 = \frac{π}{2}

\frac{π}{6} \cdot 3

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 3}{6}

Cancel the common factor:

3

= \frac{π}{2}

= cos (\frac{π}{2})

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0

= \frac{71}{20} \cdot 0 + \frac{383}{20}

Simplify

= \frac{383}{20}

- cos (15 0^{\circ})

1 - \frac{1}{2} sin (2)

cos (5. 4^{\circ})

\frac{0.1 \cdot 1 0 ^{- 9}}{sin ( 1.685 )}

2 \cdot sin (1 0^{\circ})

What is the value of 3.55cos(pi/6*3)+19.15 ?
The value of 3.55cos(pi/6*3)+19.15 is 383/20