What is the value of 4/3 cos(135) ?

The value of 4/3 cos(135) is -(2sqrt(2))/3

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4/3 cos(135)

\frac{4}{3} cos (13 5^{\circ})

- \frac{2 2}{3}

Decimal Notation

- 0.94280 \dots

Solution steps

\frac{4}{3} cos (13 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}

= \frac{4}{3} (- \frac{2}{2})

Simplify

\frac{4}{3} (- \frac{2}{2}) : - \frac{2 2}{3}

\frac{4}{3} (- \frac{2}{2})

Remove parentheses:

(- a) = - a

= - \frac{4}{3} \cdot \frac{2}{2}

Cross-cancel common factor:

2

= \frac{2}{3} \cdot \frac{2}{1}

Multiply fractions:

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

= - \frac{2 2}{3 \cdot 1}

Multiply the numbers:

3 \cdot 1 = 3

= - \frac{2 2}{3}

= - \frac{2 2}{3}

tan (5 8^{\circ}) \cdot 2

arctan (1.92)

sec (\frac{155 π}{2})

- arctan (2 \cdot 0.83 \cdot 1 0^{8} \cdot 10 \cdot 1 0^{- 9} (12))

ln (1 + sin (0))