What is the value of cos(60)*8 ?

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cos(60)*8

cos (6 0^{\circ}) \cdot 8

4

Solution steps

cos (6 0^{\circ}) \cdot 8

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}

= \frac{1}{2} \cdot 8

Simplify

\frac{1}{2} \cdot 8 : 4

\frac{1}{2} \cdot 8

Convert element to fraction:

8 = \frac{8}{1}

= \frac{1}{2} \cdot \frac{8}{1}

Cross-cancel common factor:

2

= \frac{4}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 4

= 4

sin (28. 2^{\circ})

14 sin (3 6^{\circ})

4 sin^{2} (\frac{π}{2})

tan (- \frac{53 π}{6} \cdot 1)

sec (1 4^{\circ})