What is the value of 10*cos(60) ?

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10*cos(60)

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

5

Solution steps

10 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}

= 10 \cdot \frac{1}{2}

Simplify

10 \cdot \frac{1}{2} : 5

10 \cdot \frac{1}{2}

Convert element to fraction:

10 = \frac{10}{1}

= \frac{1}{2} \cdot \frac{10}{1}

Cross-cancel common factor:

2

= \frac{5}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 5

= 5

sin (\frac{2 π}{3} + \frac{5 π}{6})

cos (\frac{25 π}{6})

- 4 sin (\frac{2 π}{3})

arcsin (10)

sin (0.9)