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

The value of sin(2arctan(2)) is 4/5

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sin(2arctan(2))

sin (2 arctan (2))

\frac{4}{5}

Decimal Notation

0.8

Solution steps

sin (2 arctan (2))

Rewrite using trig identities:

2 sin (arctan (2)) cos (arctan (2))

sin (2 arctan (2))

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (arctan (2)) cos (arctan (2))

= 2 sin (arctan (2)) cos (arctan (2))

Rewrite using trig identities:

sin (arctan (2)) = \frac{2 5}{5}

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{2 5}{5}

Rewrite using trig identities:

cos (arctan (2)) = \frac{5}{5}

cos (arctan (2))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{5}{5}

= 2 \cdot \frac{2 5}{5} \cdot \frac{5}{5}

Simplify

2 \cdot \frac{2 5}{5} \cdot \frac{5}{5} : \frac{4}{5}

2 \cdot \frac{2 5}{5} \cdot \frac{5}{5}

Multiply fractions:

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

= \frac{2 5 5 \cdot 2}{5 \cdot 5}

255 \cdot 2 = 20

255 \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 455

Apply radical rule:

a a = a

55 = 5

= 4 \cdot 5

Multiply the numbers:

4 \cdot 5 = 20

= 20

= \frac{20}{5 \cdot 5}

Multiply the numbers:

5 \cdot 5 = 25

= \frac{20}{25}

Cancel the common factor:

5

= \frac{4}{5}

= \frac{4}{5}

8 π - 12 arctan (2) - 8

\frac{cot ( π )}{4}

sin (0) + sin (1)

sin (\frac{π}{2} - π)

12 sin (2 0^{\circ})