What is the value of sin(2arctan(3/4)) ?

The value of sin(2arctan(3/4)) is 24/25

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sin(2arctan(3/4))

sin (2 arctan (\frac{3}{4}))

\frac{24}{25}

Decimal Notation

0.96

Solution steps

sin (2 arctan (\frac{3}{4}))

Rewrite using trig identities:

2 sin (arctan (\frac{3}{4})) cos (arctan (\frac{3}{4}))

sin (2 arctan (\frac{3}{4}))

Use the Double Angle identity:

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

= 2 sin (arctan (\frac{3}{4})) cos (arctan (\frac{3}{4}))

= 2 sin (arctan (\frac{3}{4})) cos (arctan (\frac{3}{4}))

Rewrite using trig identities:

sin (arctan (\frac{3}{4})) = \frac{3}{5}

sin (arctan (\frac{3}{4}))

Rewrite using trig identities:

sin (arctan (\frac{3}{4})) = \frac{( \frac{3}{4} ) 1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{3}{4} ) 1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

= \frac{\frac{3}{4} 1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

Simplify

= \frac{3}{5}

Rewrite using trig identities:

cos (arctan (\frac{3}{4})) = \frac{4}{5}

cos (arctan (\frac{3}{4}))

Rewrite using trig identities:

cos (arctan (\frac{3}{4})) = \frac{1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

Use the following identity:

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

= \frac{1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

= \frac{1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

Simplify

= \frac{4}{5}

= 2 \cdot \frac{3}{5} \cdot \frac{4}{5}

Simplify

2 \cdot \frac{3}{5} \cdot \frac{4}{5} : \frac{24}{25}

2 \cdot \frac{3}{5} \cdot \frac{4}{5}

Convert element to fraction:

2 = \frac{2}{1}

= \frac{2}{1} \cdot \frac{3}{5} \cdot \frac{4}{5}

Multiply fractions:

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

= \frac{2 \cdot 3 \cdot 4}{1 \cdot 5 \cdot 5}

Multiply the numbers:

2 \cdot 3 \cdot 4 = 24

= \frac{24}{1 \cdot 5 \cdot 5}

Multiply the numbers:

1 \cdot 5 \cdot 5 = 25

= \frac{24}{25}

= \frac{24}{25}

cos^{2} (\frac{π}{12}) - sin^{2} (\frac{π}{12})

sin (π (1))

sin (\frac{π}{2}) + \frac{π}{2} cos (\frac{π}{2})

\frac{10}{sin ( 5 5 ^{\circ} )}

sin (\frac{π}{11})

What is the value of sin(2arctan(3/4)) ?
The value of sin(2arctan(3/4)) is 24/25