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

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

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cos(2arccos(-1/2))

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

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

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 (arctan (- \frac{5}{3}))

tan (arcsin (\frac{3}{5}) + arccos (- 1))

arccos (\frac{24}{25})

sin^{8} (\frac{π}{2})

sin (3 0^{\circ}) + sin (3 0^{\circ})

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