What is the value of sin(arcsin(0)-arccos(1/2)) ?

The value of sin(arcsin(0)-arccos(1/2)) is -(sqrt(3))/2

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sin(arcsin(0)-arccos(1/2))

sin (arcsin (0) - arccos (\frac{1}{2}))

- \frac{3}{2}

Decimal Notation

- 0.86602 \dots

Solution steps

sin (arcsin (0) - arccos (\frac{1}{2}))

Rewrite using trig identities:

sin (arcsin (0)) cos (arccos (\frac{1}{2})) - cos (arcsin (0)) sin (arccos (\frac{1}{2}))

sin (arcsin (0) - arccos (\frac{1}{2}))

Use the Angle Difference identity:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

= sin (arcsin (0)) cos (arccos (\frac{1}{2})) - cos (arcsin (0)) sin (arccos (\frac{1}{2}))

= sin (arcsin (0)) cos (arccos (\frac{1}{2})) - cos (arcsin (0)) sin (arccos (\frac{1}{2}))

Rewrite using trig identities:

sin (arcsin (0)) = 0

Use the following identity:

sin (arcsin (x)) = x

= 0

Rewrite using trig identities:

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

Use the following identity:

cos (arccos (x)) = x

= \frac{1}{2}

Rewrite using trig identities:

cos (arcsin (0)) = 1

cos (arcsin (0))

Rewrite using trig identities:

cos (arcsin (0)) = 1 - 0^{2}

Use the following identity:

cos (arcsin (x)) = 1 - x^{2}

= 1 - 0^{2}

= 1 - 0^{2}

Simplify

= 1

Rewrite using trig identities:

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

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

Rewrite using trig identities:

sin (arccos (\frac{1}{2})) = 1 - (\frac{1}{2})^{2}

Use the following identity:

sin (arccos (x)) = 1 - x^{2}

= 1 - (\frac{1}{2})^{2}

= 1 - (\frac{1}{2})^{2}

Simplify

= \frac{3}{2}

= 0 \cdot \frac{1}{2} - 1 \cdot \frac{3}{2}

Simplify

= - \frac{3}{2}

\frac{tan ( 5 1 ^{\circ} )}{1 - tan ( 5 1 ^{\circ} )}

csc (arccos (- \frac{5}{8}))

\frac{( cos ( 4 5 ^{\circ} ) ) ^{2} + 3 csc ( 3 7 ^{\circ} )}{2 tan ( 4 5 ^{\circ} )}

cos^{2} (21 0^{\circ})

sin (\frac{π}{4}) sin (\frac{π}{12})

What is the value of sin(arcsin(0)-arccos(1/2)) ?
The value of sin(arcsin(0)-arccos(1/2)) is -(sqrt(3))/2