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

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

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sin(arcsin((sqrt(3))/2)+arccos(1))

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

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

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

Rewrite using trig identities:

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

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

Use the Angle Sum identity:

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

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

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

Rewrite using trig identities:

sin (arcsin (\frac{3}{2})) = \frac{3}{2}

Use the following identity:

sin (arcsin (x)) = x

= \frac{3}{2}

Rewrite using trig identities:

cos (arccos (1)) = 1

Use the following identity:

cos (arccos (x)) = x

= 1

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{1}{2}

Rewrite using trig identities:

sin (arccos (1)) = 0

sin (arccos (1))

Rewrite using trig identities:

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

Use the following identity:

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

= 1 - 1^{2}

= 1 - 1^{2}

Simplify

= 0

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

Simplify

= \frac{3}{2}

sin (11 6^{\circ})

2 cos (2 \cdot 0)

8 cos (12 0^{\circ})

cos (\frac{4 π}{4})

csc (- 3 π)

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