What is the value of sin(pi/3-arcsin(-1/2)) ?

The value of sin(pi/3-arcsin(-1/2)) is 1

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sin(pi/3-arcsin(-1/2))

sin (\frac{π}{3} - arcsin (- \frac{1}{2}))

1

Solution steps

sin (\frac{π}{3} - arcsin (- \frac{1}{2}))

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

Rewrite using trig identities:

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

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Rewrite using trig identities:

sin (arcsin (\frac{1}{2})) = \frac{1}{2}

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

Simplify

\frac{3}{2} \cdot \frac{3}{2} + \frac{1}{2} \cdot \frac{1}{2} : 1

= 1

sec (4 5^{\circ}) csc (4 5^{\circ})

2 \cdot cos (12 0^{\circ})

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

- 2 e^{0} sin (0)

cos (6 0^{\circ}) + sec (6 0^{\circ})

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