What is the value of sin((2pi)/3+(5pi)/6) ?

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

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sin((2pi)/3+(5pi)/6)

sin (\frac{2 π}{3} + \frac{5 π}{6})

- 1

Solution steps

sin (\frac{2 π}{3} + \frac{5 π}{6})

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

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

Simplify

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

= - 1

cos (\frac{25 π}{6})

- 4 sin (\frac{2 π}{3})

arcsin (10)

sin (0.9)

arcsin (\frac{4}{3})

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