What is the value of 3.5cos(45) ?

The value of 3.5cos(45) is (7sqrt(2))/4

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3.5cos(45)

3.5 cos (4 5^{\circ})

\frac{7 2}{4}

Decimal Notation

2.47487 \dots

Solution steps

3.5 cos (4 5^{\circ})

= \frac{7}{2} cos (4 5^{\circ})

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= \frac{7}{2} \cdot \frac{2}{2}

Simplify

\frac{7}{2} \cdot \frac{2}{2} : \frac{7 2}{4}

\frac{7}{2} \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{7 2}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{7 2}{4}

= \frac{7 2}{4}

arcsin (\frac{1}{7})

arccos (sin (- \frac{4 π}{3}))

sin (2 arctan (\frac{4}{3}))

sin (21 5^{\circ})

9 sin (\frac{2 π}{3})