What is the value of cos(arctan(-2/9)) ?

The value of cos(arctan(-2/9)) is (9sqrt(85))/(85)

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cos(arctan(-2/9))

cos (arctan (- \frac{2}{9}))

\frac{9 85}{85}

Decimal Notation

0.97618 \dots

Solution steps

cos (arctan (- \frac{2}{9}))

Rewrite using trig identities:

cos (arctan (- \frac{2}{9})) = \frac{1 + ( - \frac{2}{9} ) ^{2}}{1 + ( - \frac{2}{9} ) ^{2}}

Use the following identity:

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

= \frac{1 + ( - \frac{2}{9} ) ^{2}}{1 + ( - \frac{2}{9} ) ^{2}}

= \frac{1 + ( - \frac{2}{9} ) ^{2}}{1 + ( - \frac{2}{9} ) ^{2}}

Simplify

= \frac{9 85}{85}

20 sin (8 0^{\circ})

cos (26. 5^{\circ})

\frac{113}{36.5 \cdot cos ( 3 0 ^{\circ} )}

\frac{sin ( 301 5 ^{\circ} ) tan ( 429 0 ^{\circ} )}{cos ( 273 0 ^{\circ} )}

sinh (- arccosh (2))

What is the value of cos(arctan(-2/9)) ?
The value of cos(arctan(-2/9)) is (9sqrt(85))/(85)