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

The value of cos(arctan(-sqrt(3))) is 1/2

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cos(arctan(-sqrt(3)))

cos (arctan (- 3))

\frac{1}{2}

Decimal Notation

0.5

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{1}{2}

0 - sin (0)

cot (- 28 0^{\circ})

sin (2 (\frac{π}{3}))

csc (\frac{17 π}{12})

cos (arccos (53))

What is the value of cos(arctan(-sqrt(3))) ?
The value of cos(arctan(-sqrt(3))) is 1/2