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}))

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{3}{4}) = - arctan (\frac{3}{4})

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

Use the following property:

cos (- x) = cos (x)

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

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

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{3}{4}) = - arctan (\frac{3}{4})

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

Use the following property:

sin (- x) = - sin (x)

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

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

Simplify

= - 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}

arctan (\frac{- 13.79}{25.54})

cos (5 (0))

6 sin (9 0^{\circ})

cos (- 108 0^{\circ})

7 cos (6 5^{\circ})

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