What is the value of sin(arcsin(3/5)-arccos(-4/5)) ?

The value of sin(arcsin(3/5)-arccos(-4/5)) is -24/25

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sin(arcsin(3/5)-arccos(-4/5))

sin (arcsin (\frac{3}{5}) - arccos (- \frac{4}{5}))

- \frac{24}{25}

Solution steps

sin (arcsin (\frac{3}{5}) - arccos (- \frac{4}{5}))

Rewrite using trig identities:

sin (arcsin (\frac{3}{5})) cos (arccos (- \frac{4}{5})) - cos (arcsin (\frac{3}{5})) sin (arccos (- \frac{4}{5}))

= sin (arcsin (\frac{3}{5})) cos (arccos (- \frac{4}{5})) - cos (arcsin (\frac{3}{5})) sin (arccos (- \frac{4}{5}))

Rewrite using trig identities:

sin (arcsin (\frac{3}{5})) = \frac{3}{5}

Rewrite using trig identities:

cos (arccos (- \frac{4}{5})) = - \frac{4}{5}

Rewrite using trig identities:

cos (arcsin (\frac{3}{5})) = \frac{4}{5}

Rewrite using trig identities:

sin (arccos (- \frac{4}{5})) = \frac{3}{5}

= \frac{3}{5} (- \frac{4}{5}) - \frac{4}{5} \cdot \frac{3}{5}

Simplify

\frac{3}{5} (- \frac{4}{5}) - \frac{4}{5} \cdot \frac{3}{5} : - \frac{24}{25}

= - \frac{24}{25}

2 sin (\frac{11 π}{6})

10 cos (9 0^{\circ})

cot (2 1^{\circ})

arcsin (0.89)

arcsin (\frac{3}{9})

What is the value of sin(arcsin(3/5)-arccos(-4/5)) ?
The value of sin(arcsin(3/5)-arccos(-4/5)) is -24/25