What is the value of cos(arctan(-2)) ?

The value of cos(arctan(-2)) is (sqrt(5))/5

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cos(arctan(-2))

cos (arctan (- 2))

\frac{5}{5}

Decimal Notation

0.4472135955

Solution steps

cos (arctan (- 2))

Rewrite using trig identities:

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

Use the following identity:

cos (arctan (x)) = \frac{1 + x ^{2}}{1 + x ^{2}}

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

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

Simplify

= \frac{5}{5}

cos (\frac{13 π}{15}) cos (- \frac{π}{5}) - sin (\frac{13 π}{15}) sin (- \frac{π}{5})

5 cos (4 5^{\circ})

sin (\frac{3 π}{6})

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

cot (\frac{19 π}{6})

What is the value of cos(arctan(-2)) ?
The value of cos(arctan(-2)) is (sqrt(5))/5