What is the value of sin((2pi)/3+pi/4) ?

The value of sin((2pi)/3+pi/4) is (sqrt(2)(sqrt(3)-1))/4

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sin((2pi)/3+pi/4)

sin (\frac{2 π}{3} + \frac{π}{4})

\frac{2 ( 3 - 1 )}{4}

Solution steps

sin (\frac{2 π}{3} + \frac{π}{4})

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

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

Simplify

\frac{3}{2} \cdot \frac{2}{2} + (- \frac{1}{2}) \frac{2}{2} : \frac{2 ( 3 - 1 )}{4}

= \frac{2 ( 3 - 1 )}{4}

cos^{2} (2 5^{\circ}) - sin^{2} (2 5^{\circ})

tan (6 2^{\circ}) (15)

\frac{2 ( cos ( 3 0 ^{\circ} ) + i sin ( 3 0 ^{\circ} ) )}{3 ( cos ( 6 0 ^{\circ} ) + i sin ( 6 0 ^{\circ} ) )}

arccot (tan (6))

- 2 cos (\frac{11 π}{6})

What is the value of sin((2pi)/3+pi/4) ?
The value of sin((2pi)/3+pi/4) is (sqrt(2)(sqrt(3)-1))/4