What is the value of cos(pi/2)-sin((5pi)/3)+tan((9pi)/4)-cos((5pi)/6)+tan((7pi)/6) ?

The value of cos(pi/2)-sin((5pi)/3)+tan((9pi)/4)-cos((5pi)/6)+tan((7pi)/6) is (sqrt(3))/3+1+sqrt(3)

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cos(pi/2)-sin((5pi)/3)+tan((9pi)/4)-cos((5pi)/6)+tan((7pi)/6)

cos (\frac{π}{2}) - sin (\frac{5 π}{3}) + tan (\frac{9 π}{4}) - cos (\frac{5 π}{6}) + tan (\frac{7 π}{6})

\frac{3}{3} + 1 + 3

Solution steps

cos (\frac{π}{2}) - sin (\frac{5 π}{3}) + tan (\frac{9 π}{4}) - cos (\frac{5 π}{6}) + tan (\frac{7 π}{6})

tan (\frac{9 π}{4}) = tan (\frac{π}{4})

= cos (\frac{π}{2}) - sin (\frac{5 π}{3}) + tan (\frac{π}{4}) - cos (\frac{5 π}{6}) + tan (\frac{7 π}{6})

tan (\frac{7 π}{6}) = tan (\frac{π}{6})

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

Use the following trivial identity:

cos (\frac{π}{2}) = 0

Rewrite using trig identities:

sin (\frac{5 π}{3}) = - \frac{3}{2}

Use the following trivial identity:

tan (\frac{π}{4}) = 1

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

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

Simplify

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

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

\frac{1}{2} sin (2 \cdot \frac{π}{4})

arccos (cos (\frac{- π}{6}))

sin (28.0 7^{\circ})

5 cos (54 0^{\circ})

csc (0.9)

What is the value of cos(pi/2)-sin((5pi)/3)+tan((9pi)/4)-cos((5pi)/6)+tan((7pi)/6) ?
The value of cos(pi/2)-sin((5pi)/3)+tan((9pi)/4)-cos((5pi)/6)+tan((7pi)/6) is (sqrt(3))/3+1+sqrt(3)