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

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

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sin(arcsin(0)+arccos((sqrt(3))/2))

sin (arcsin (0) + arccos (\frac{3}{2}))

\frac{1}{2}

Decimal Notation

0.5

Solution steps

sin (arcsin (0) + arccos (\frac{3}{2}))

Rewrite using trig identities:

sin (arcsin (0)) cos (arccos (\frac{3}{2})) + cos (arcsin (0)) sin (arccos (\frac{3}{2}))

sin (arcsin (0) + arccos (\frac{3}{2}))

Use the Angle Sum identity:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= sin (arcsin (0)) cos (arccos (\frac{3}{2})) + cos (arcsin (0)) sin (arccos (\frac{3}{2}))

= sin (arcsin (0)) cos (arccos (\frac{3}{2})) + cos (arcsin (0)) sin (arccos (\frac{3}{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{3}{2})) = \frac{3}{2}

Use the following identity:

cos (arccos (x)) = x

= \frac{3}{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{3}{2})) = \frac{1}{2}

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{1}{2}

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

Simplify

= \frac{1}{2}

sin (2 9^{\circ}) tan (4 6^{\circ})

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

2 cos (\frac{5 π}{2})

sec (\frac{π}{4}) tan (\frac{π}{4}) - 2 sec^{2} (\frac{π}{4})

\frac{5}{tan ( 4 0 ^{\circ} )}

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