What is the value of (cos(pi/2)-cos((4pi)/3))/(2sin((5pi)/6)) ?

The value of (cos(pi/2)-cos((4pi)/3))/(2sin((5pi)/6)) is 1/2

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(cos(pi/2)-cos((4pi)/3))/(2sin((5pi)/6))

\frac{cos ( \frac{π}{2} ) - cos ( \frac{4 π}{3} )}{2 sin ( \frac{5 π}{6} )}

\frac{1}{2}

Solution steps

\frac{cos ( \frac{π}{2} ) - cos ( \frac{4 π}{3} )}{2 sin ( \frac{5 π}{6} )}

Rewrite using trig identities:

cos (\frac{4 π}{3}) = 1 - 2 sin^{2} (\frac{2 π}{3})

= \frac{cos ( \frac{π}{2} ) - ( 1 - 2 sin ^{2} ( \frac{2 π}{3} ) )}{2 sin ( \frac{5 π}{6} )}

Simplify

= \frac{cos ( \frac{π}{2} ) - 1 + 2 sin ^{2} ( \frac{2 π}{3} )}{2 sin ( \frac{5 π}{6} )}

Use the following trivial identity:

cos (\frac{π}{2}) = 0

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

= \frac{0 - 1 + 2 ( \frac{3}{2} ) ^{2}}{2 \cdot \frac{1}{2}}

Simplify

\frac{0 - 1 + 2 ( \frac{3}{2} ) ^{2}}{2 \cdot \frac{1}{2}} : \frac{1}{2}

= \frac{1}{2}

35 sin (1 0^{\circ}) - (9.8 \cdot 7.5)

arcsin (\frac{3}{18})

cot (12 7^{\circ})

arcsin (0.69264)

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

What is the value of (cos(pi/2)-cos((4pi)/3))/(2sin((5pi)/6)) ?
The value of (cos(pi/2)-cos((4pi)/3))/(2sin((5pi)/6)) is 1/2