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

The value of cos(2arcsin(2/5)) is 17/25

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(2arcsin(2/5))

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

\frac{17}{25}

Decimal Notation

0.68

Solution steps

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

Rewrite using trig identities:

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

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

Use the Double Angle identity:

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

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

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

Rewrite using trig identities:

cos (arcsin (\frac{2}{5})) = \frac{21}{5}

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{21}{5}

= 2 (\frac{21}{5})^{2} - 1

Simplify

2 (\frac{21}{5})^{2} - 1 : \frac{17}{25}

2 (\frac{21}{5})^{2} - 1

2 (\frac{21}{5})^{2} = \frac{42}{25}

2 (\frac{21}{5})^{2}

(\frac{21}{5})^{2} = \frac{21}{5 ^{2}}

(\frac{21}{5})^{2}

Apply exponent rule:

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

= \frac{( 21 ) ^{2}}{5 ^{2}}

(21)^{2} : 21

Apply radical rule:

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

= (2 1^{\frac{1}{2}})^{2}

Apply exponent rule:

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

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

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

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

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 21

= \frac{21}{5 ^{2}}

= 2 \cdot \frac{21}{5 ^{2}}

Multiply fractions:

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

= \frac{21 \cdot 2}{5 ^{2}}

Multiply the numbers:

21 \cdot 2 = 42

= \frac{42}{5 ^{2}}

5^{2} = 25

= \frac{42}{25}

= \frac{42}{25} - 1

Convert element to fraction:

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

= - \frac{1 \cdot 25}{25} + \frac{42}{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 + 42}{25}

- 1 \cdot 25 + 42 = 17

- 1 \cdot 25 + 42

Multiply the numbers:

1 \cdot 25 = 25

= - 25 + 42

Add/Subtract the numbers:

- 25 + 42 = 17

= 17

= \frac{17}{25}

= \frac{17}{25}

- 4 cos^{3} (- 0.74) sin (- 0.74) - 4 (- 0.74)

0.2 \cdot sin (3 0^{\circ})

sin (202 2^{\circ})

\frac{sin ( 8 )}{30}

cot (\frac{3}{2})

What is the value of cos(2arcsin(2/5)) ?
The value of cos(2arcsin(2/5)) is 17/25