What is the value of cos(arctan((-2)/3)) ?

The value of cos(arctan((-2)/3)) is (3sqrt(13))/(13)

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cos(arctan((-2)/3))

cos (arctan (\frac{- 2}{3}))

\frac{3 13}{13}

Decimal Notation

0.83205 \dots

Solution steps

cos (arctan (\frac{- 2}{3}))

Rewrite using trig identities:

cos (arctan (\frac{- 2}{3})) = \frac{1 + ( \frac{- 2}{3} ) ^{2}}{1 + ( \frac{- 2}{3} ) ^{2}}

Use the following identity:

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

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

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

Simplify

= \frac{3 13}{13}

2 sin (2) - 1

sin (12. 7^{\circ})

sinh (((2 \cdot 2.47832) - 4) - 0.7 \cdot 2.47832)

cos (11 4^{\circ})

tan (\frac{6}{12})

What is the value of cos(arctan((-2)/3)) ?
The value of cos(arctan((-2)/3)) is (3sqrt(13))/(13)