What is the value of cos(2arccos(-0.5)) ?

The value of cos(2arccos(-0.5)) is -1/2

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cos(2arccos(-0.5))

cos (2 arccos (- 0.5))

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

cos (2 arccos (- 0.5))

= cos (2 arccos (- \frac{1}{2}))

Rewrite using trig identities:

2 cos^{2} (arccos (- \frac{1}{2})) - 1

cos (2 arccos (- \frac{1}{2}))

Use the Double Angle identity:

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

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

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

Rewrite using trig identities:

cos (arccos (- \frac{1}{2})) = - \frac{1}{2}

Use the following identity:

cos (arccos (x)) = x

= - \frac{1}{2}

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

Simplify

2 (- \frac{1}{2})^{2} - 1 : - \frac{1}{2}

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

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

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

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

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

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

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

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

Apply exponent rule:

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

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

Apply rule

1^{a} = 1

1^{2} = 1

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

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2}{2 ^{2}}

Cancel the common factor:

2

= \frac{1}{2}

= \frac{1}{2} - 1

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

- 1 \cdot 2 + 1 = - 1

- 1 \cdot 2 + 1

Multiply the numbers:

1 \cdot 2 = 2

= - 2 + 1

Add/Subtract the numbers:

- 2 + 1 = - 1

= - 1

= \frac{- 1}{2}

Apply the fraction rule:

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

= - \frac{1}{2}

= - \frac{1}{2}

sin (π + i \frac{π}{2})

arcsin (\frac{sin ( 4 5 ^{\circ} )}{1.41})

5 sin (5 3^{\circ})

arccos (\frac{1}{14})

arctan (\frac{2.55}{9.8} + 0.5)

What is the value of cos(2arccos(-0.5)) ?
The value of cos(2arccos(-0.5)) is -1/2