What is the value of 1.5cos(30) ?

The value of 1.5cos(30) is (3sqrt(3))/4

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1.5cos(30)

1.5 cos (3 0^{\circ})

\frac{3 3}{4}

Decimal Notation

1.29903 \dots

Solution steps

1.5 cos (3 0^{\circ})

= \frac{3}{2} cos (3 0^{\circ})

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\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{3}{2}

= \frac{3}{2} \cdot \frac{3}{2}

Simplify

\frac{3}{2} \cdot \frac{3}{2} : \frac{3 3}{4}

\frac{3}{2} \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 3}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{3 3}{4}

= \frac{3 3}{4}

sin^{2} (\frac{7 π}{6})

csc (\frac{9 π}{8})

tan (\frac{5 π}{6} + \frac{7 π}{4})

2 sec (\frac{π}{3})

tan (2 arccos (\frac{4}{5}))