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

The value of 8cos(-45) is 4sqrt(2)

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8cos(-45)

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

42

Decimal Notation

5.65685 \dots

Solution steps

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

Rewrite using trig identities:

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

cos (- 4 5^{\circ})

Use the following property:

cos (- x) = cos (x)

cos (- 4 5^{\circ}) = cos (4 5^{\circ})

= 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{2}{2}

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

Simplify

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

= 42

sin (3 π \frac{1}{2})

cot (- \frac{7 π}{9})

arcsin (\frac{11}{6})

arctan (\frac{9}{24})

1 - cos (1)