What is the value of 5cos(30)-8sin(45) ?

The value of 5cos(30)-8sin(45) is (5sqrt(3))/2-4sqrt(2)

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5cos(30)-8sin(45)

5 cos (3 0^{\circ}) - 8 sin (4 5^{\circ})

\frac{5 3}{2} - 42

Decimal Notation

- 1.32672 \dots

Solution steps

5 cos (3 0^{\circ}) - 8 sin (4 5^{\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}

Use the following trivial identity:

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

sin (4 5^{\circ})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= 5 \cdot \frac{3}{2} - 8 \cdot \frac{2}{2}

Simplify

5 \cdot \frac{3}{2} - 8 \cdot \frac{2}{2} : \frac{5 3}{2} - 42

5 \cdot \frac{3}{2} - 8 \cdot \frac{2}{2}

5 \cdot \frac{3}{2} = \frac{5 3}{2}

5 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 5}{2}

8 \cdot \frac{2}{2} = 42

8 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 8}{2}

Divide the numbers:

\frac{8}{2} = 4

= 42

= \frac{5 3}{2} - 42

= \frac{5 3}{2} - 42

\frac{24}{tan ( 6 0 ^{\circ} )}

\frac{20}{tan ( 3 8 ^{\circ} )}

arccos (\frac{6}{43})

98 cos (3 0^{\circ})

cot (\frac{7 π}{9})

What is the value of 5cos(30)-8sin(45) ?
The value of 5cos(30)-8sin(45) is (5sqrt(3))/2-4sqrt(2)