What is the value of 120cos(60) ?

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120cos(60)

120 cos (6 0^{\circ})

60

Solution steps

120 cos (6 0^{\circ})

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 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{1}{2}

= 120 \cdot \frac{1}{2}

Simplify

120 \cdot \frac{1}{2} : 60

120 \cdot \frac{1}{2}

Convert element to fraction:

120 = \frac{120}{1}

= \frac{1}{2} \cdot \frac{120}{1}

Cross-cancel common factor:

2

= \frac{60}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 60

= 60

csc (\frac{- π}{3})

120 sin (3 0^{\circ})

csc (\frac{- π}{2})

sin (arcsin (\frac{8}{17}) + arccos (- \frac{3}{5}))

8 \cdot cos (4 0^{\circ})