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}

sin (3 0^{\circ}) \cdot 5

3 cos (\frac{5 π}{4})

\frac{2 tan ( \frac{π}{10} )}{1 - tan ^{2} ( \frac{π}{10} )}

- sin (5)

- 4 cos (\frac{π}{4})

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