What is the value of cos(2arcsin(4/5)) ?

The value of cos(2arcsin(4/5)) is -7/25

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cos(2arcsin(4/5))

cos (2 arcsin (\frac{4}{5}))

- \frac{7}{25}

Decimal Notation

- 0.28

Solution steps

cos (2 arcsin (\frac{4}{5}))

Rewrite using trig identities:

2 cos^{2} (arcsin (\frac{4}{5})) - 1

cos (2 arcsin (\frac{4}{5}))

Use the Double Angle identity:

cos (2 x) = 2 cos^{2} (x) - 1

= 2 cos^{2} (arcsin (\frac{4}{5})) - 1

= 2 cos^{2} (arcsin (\frac{4}{5})) - 1

Rewrite using trig identities:

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

cos (arcsin (\frac{4}{5}))

Rewrite using trig identities:

cos (arcsin (\frac{4}{5})) = 1 - (\frac{4}{5})^{2}

Use the following identity:

cos (arcsin (x)) = 1 - x^{2}

= 1 - (\frac{4}{5})^{2}

= 1 - (\frac{4}{5})^{2}

Simplify

= \frac{3}{5}

= 2 (\frac{3}{5})^{2} - 1

Simplify

2 (\frac{3}{5})^{2} - 1 : - \frac{7}{25}

2 (\frac{3}{5})^{2} - 1

2 (\frac{3}{5})^{2} = \frac{18}{25}

2 (\frac{3}{5})^{2}

(\frac{3}{5})^{2} = \frac{3 ^{2}}{5 ^{2}}

(\frac{3}{5})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{3 ^{2}}{5 ^{2}}

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

Multiply fractions:

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

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

3^{2} \cdot 2 = 18

3^{2} \cdot 2

3^{2} = 9

= 9 \cdot 2

Multiply the numbers:

9 \cdot 2 = 18

= 18

= \frac{18}{5 ^{2}}

5^{2} = 25

= \frac{18}{25}

= \frac{18}{25} - 1

Convert element to fraction:

1 = \frac{1 \cdot 25}{25}

= - \frac{1 \cdot 25}{25} + \frac{18}{25}

Since the denominators are equal, combine the fractions:

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

= \frac{- 1 \cdot 25 + 18}{25}

- 1 \cdot 25 + 18 = - 7

- 1 \cdot 25 + 18

Multiply the numbers:

1 \cdot 25 = 25

= - 25 + 18

Add/Subtract the numbers:

- 25 + 18 = - 7

= - 7

= \frac{- 7}{25}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{7}{25}

= - \frac{7}{25}

sec (- 27 0^{\circ})

cot (\frac{- 5 π}{6})

arcsin (- \frac{1}{2}) + arccos (1)

sin^{4} (\frac{π}{2})

arccos (0.1)

What is the value of cos(2arcsin(4/5)) ?
The value of cos(2arcsin(4/5)) is -7/25