What is the value of sin(arcsin(2/3)+arccos(1/2)) ?

The value of sin(arcsin(2/3)+arccos(1/2)) is 1/3+(sqrt(15))/6

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sin(arcsin(2/3)+arccos(1/2))

sin (arcsin (\frac{2}{3}) + arccos (\frac{1}{2}))

\frac{1}{3} + \frac{15}{6}

Solution steps

sin (arcsin (\frac{2}{3}) + arccos (\frac{1}{2}))

Rewrite using trig identities:

sin (arcsin (\frac{2}{3})) cos (arccos (\frac{1}{2})) + cos (arcsin (\frac{2}{3})) sin (arccos (\frac{1}{2}))

= sin (arcsin (\frac{2}{3})) cos (arccos (\frac{1}{2})) + cos (arcsin (\frac{2}{3})) sin (arccos (\frac{1}{2}))

Rewrite using trig identities:

sin (arcsin (\frac{2}{3})) = \frac{2}{3}

Rewrite using trig identities:

cos (arccos (\frac{1}{2})) = \frac{1}{2}

Rewrite using trig identities:

cos (arcsin (\frac{2}{3})) = \frac{5}{3}

Rewrite using trig identities:

sin (arccos (\frac{1}{2})) = \frac{3}{2}

= \frac{2}{3} \cdot \frac{1}{2} + \frac{5}{3} \cdot \frac{3}{2}

Simplify

\frac{2}{3} \cdot \frac{1}{2} + \frac{5}{3} \cdot \frac{3}{2} : \frac{1}{3} + \frac{15}{6}

= \frac{1}{3} + \frac{15}{6}

cot (7 3^{\circ})

\frac{183 \cdot 9.8}{sin ( 2 \cdot 45 )}

4 (cos (\frac{5 π}{6}) + i sin (\frac{5 π}{6}))

arctan (- 0.9)

3 cos (\frac{5 π}{3})

What is the value of sin(arcsin(2/3)+arccos(1/2)) ?
The value of sin(arcsin(2/3)+arccos(1/2)) is 1/3+(sqrt(15))/6