What is the value of cot((2pi)/3)-sin((3pi)/2) ?

The value of cot((2pi)/3)-sin((3pi)/2) is -(sqrt(3))/3+1

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cot((2pi)/3)-sin((3pi)/2)

cot (\frac{2 π}{3}) - sin (\frac{3 π}{2})

- \frac{3}{3} + 1

Solution steps

cot (\frac{2 π}{3}) - sin (\frac{3 π}{2})

Rewrite using trig identities:

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

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

Use the following trivial identity:

cot (\frac{2 π}{3}) = - \frac{3}{3}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

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

Simplify

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

= - \frac{3}{3} + 1

sin (51.3 4^{\circ})

\frac{sin ( 5 ( - 0.1 ) )}{- 0.1}

sin^{2} (\frac{17 π}{2}) + cos^{2} (\frac{17 π}{2})

sin ((\frac{π}{2})^{2})

sin (\frac{19}{12} π)

What is the value of cot((2pi)/3)-sin((3pi)/2) ?
The value of cot((2pi)/3)-sin((3pi)/2) is -(sqrt(3))/3+1