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

The value of sin(arctan(sqrt(2))) is (sqrt(6))/3

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sin(arctan(sqrt(2)))

sin (arctan (2))

\frac{6}{3}

Decimal Notation

0.81649 \dots

Solution steps

sin (arctan (2))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{6}{3}

sin (4 5^{\circ} + 18 0^{\circ})

cosh (- ln (2))

cos (5 \frac{π}{2})

\frac{3}{cos ( 4 0 ^{\circ} )}

2 (cos (\frac{5 π}{6}) + i sin (\frac{5 π}{6}))

What is the value of sin(arctan(sqrt(2))) ?
The value of sin(arctan(sqrt(2))) is (sqrt(6))/3