What is the value of sin(arctan(sqrt(3))) ?

The value of sin(arctan(sqrt(3))) is (sqrt(3))/2

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sin(arctan(sqrt(3)))

sin (arctan (3))

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

sin (arctan (3))

Rewrite using trig identities:

sin (arctan (3)) = \frac{3 1 + ( 3 ) ^{2}}{1 + ( 3 ) ^{2}}

Use the following identity:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

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

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

Simplify

= \frac{3}{2}

cos (\frac{π}{4}) + cos (\frac{π}{3})

sin (1 4^{\circ})

1 - cos (0)

sin (6 3^{\circ})

π sin (π)

What is the value of sin(arctan(sqrt(3))) ?
The value of sin(arctan(sqrt(3))) is (sqrt(3))/2