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

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

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

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

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

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

Rewrite using trig identities:

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

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

Use the Angle Sum identity:

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

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

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

Rewrite using trig identities:

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

Use the following identity:

sin (arcsin (x)) = x

= \frac{1}{2}

Rewrite using trig identities:

cos (arccos (0)) = 0

Use the following identity:

cos (arccos (x)) = x

= 0

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{3}{2}

Rewrite using trig identities:

sin (arccos (0)) = 1

sin (arccos (0))

Rewrite using trig identities:

sin (arccos (0)) = 1 - 0^{2}

Use the following identity:

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

= 1 - 0^{2}

= 1 - 0^{2}

Simplify

= 1

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

Simplify

= \frac{3}{2}

\frac{1}{cos ^{2} ( 0 )}

2 sec (\frac{π}{4})

arctan (\frac{7}{8})

csc (\frac{17 π}{6})

20 cos (4 5^{\circ})

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