What is the value of 6cos(135)-6cos(45) ?

The value of 6cos(135)-6cos(45) is -6sqrt(2)

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6cos(135)-6cos(45)

6 cos (13 5^{\circ}) - 6 cos (4 5^{\circ})

- 62

Decimal

- 8.48528 \dots

Solution steps

6 cos (13 5^{\circ}) - 6 cos (4 5^{\circ})

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

cos (13 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}

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}

= 6 (- \frac{2}{2}) - 6 \cdot \frac{2}{2}

Simplify

6 (- \frac{2}{2}) - 6 \cdot \frac{2}{2} : - 62

6 (- \frac{2}{2}) - 6 \cdot \frac{2}{2}

Remove parentheses:

(- a) = - a

= - 6 \cdot \frac{2}{2} - 6 \cdot \frac{2}{2}

Add similar elements:

- 6 \cdot \frac{2}{2} - 6 \cdot \frac{2}{2} = - 12 \cdot \frac{2}{2}

= - 12 \cdot \frac{2}{2}

Multiply fractions:

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

= - \frac{2 \cdot 12}{2}

Divide the numbers:

\frac{12}{2} = 6

= - 62

= - 62

What is the value of 6cos(135)-6cos(45) ?
The value of 6cos(135)-6cos(45) is -6sqrt(2)