What is the value of sin((3pi)/2)+tan(pi)cos(pi/2)-cot((5pi)/6)-sin((7pi)/6) ?

The value of sin((3pi)/2)+tan(pi)cos(pi/2)-cot((5pi)/6)-sin((7pi)/6) is -1/2+sqrt(3)

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sin((3pi)/2)+tan(pi)cos(pi/2)-cot((5pi)/6)-sin((7pi)/6)

sin (\frac{3 π}{2}) + tan (π) cos (\frac{π}{2}) - cot (\frac{5 π}{6}) - sin (\frac{7 π}{6})

- \frac{1}{2} + 3

Solution steps

sin (\frac{3 π}{2}) + tan (π) cos (\frac{π}{2}) - cot (\frac{5 π}{6}) - sin (\frac{7 π}{6})

tan (π) = tan (0)

= sin (\frac{3 π}{2}) + tan (0) cos (\frac{π}{2}) - cot (\frac{5 π}{6}) - sin (\frac{7 π}{6})

Rewrite as

= sin (\frac{3 π}{2}) - sin (\frac{7 π}{6}) + tan (0) cos (\frac{π}{2}) - cot (\frac{5 π}{6})

Rewrite using trig identities:

sin (\frac{3 π}{2}) - sin (\frac{7 π}{6}) = 2 sin (\frac{π}{6}) cos (\frac{4 π}{3})

= 2 sin (\frac{π}{6}) cos (\frac{4 π}{3}) + tan (0) cos (\frac{π}{2}) - cot (\frac{5 π}{6})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

Rewrite using trig identities:

cos (\frac{4 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

tan (0) = 0

Use the following trivial identity:

cos (\frac{π}{2}) = 0

Use the following trivial identity:

cot (\frac{5 π}{6}) = - 3

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

Simplify

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

= - \frac{1}{2} + 3

cos (\frac{π}{3}) - cos (0)

5 sin (5 π)

cos (1.25)

3 sin^{2} (4 5^{\circ}) + 4 cos^{2} (4 5^{\circ})

sin (\frac{π}{5}) cos (\frac{2 π}{15}) + cos (\frac{π}{5}) sin (\frac{2 π}{15})

What is the value of sin((3pi)/2)+tan(pi)cos(pi/2)-cot((5pi)/6)-sin((7pi)/6) ?
The value of sin((3pi)/2)+tan(pi)cos(pi/2)-cot((5pi)/6)-sin((7pi)/6) is -1/2+sqrt(3)