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

The value of cos(arctan(-3)) is (sqrt(10))/(10)

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cos(arctan(-3))

cos (arctan (- 3))

\frac{10}{10}

Decimal Notation

0.31622 \dots

Solution steps

cos (arctan (- 3))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{10}{10}

- \frac{1}{2} sin (2 π)

tan (21. 8^{\circ})

sin (9 0^{\circ}) + (cos (21 0^{\circ}) + sin (30 0^{\circ}))^{2} + sec (24 0^{\circ})

arctan (3) - arctan (2)

3 cos (21 0^{\circ})

What is the value of cos(arctan(-3)) ?
The value of cos(arctan(-3)) is (sqrt(10))/(10)