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

The value of 2sin(arctan(3)) is (3sqrt(10))/5

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2sin(arctan(3))

2 sin (arctan (3))

\frac{3 10}{5}

Decimal Notation

1.89736 \dots

Solution steps

2 sin (arctan (3))

Rewrite using trig identities:

sin (arctan (3)) = \frac{3 10}{10}

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 10}{10}

= 2 \cdot \frac{3 10}{10}

Simplify

2 \cdot \frac{3 10}{10} : \frac{3 10}{5}

2 \cdot \frac{3 10}{10}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 10 \cdot 2}{10}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{6 10}{10}

Cancel the common factor:

2

= \frac{3 10}{5}

= \frac{3 10}{5}

3.15 cos (\frac{π}{6} 7) + 19.15

2 sin (3 0^{\circ}) - tan (4 5^{\circ})

\frac{1 - tan ^{2} ( 1 5 ^{\circ} )}{1 + tan ^{2} ( 1 5 ^{\circ} )}

π (0.04)^{2} cos (3 0^{\circ}) (- 0.2)

- csc (3 0^{\circ})

What is the value of 2sin(arctan(3)) ?
The value of 2sin(arctan(3)) is (3sqrt(10))/5