cos(arctan(2)) — step-by-step solution

Let's calculate:

\cos (\arctan (2))

For real t, arctan(t) lies in (−π/2, π/2), so its cosine is positive and

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

ⅰ

\cos (\arctan (2))

\frac{1}{\sqrt{1 + 2^{2}}}

\frac{1}{\sqrt{1 + 2^{2}}}

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

2^{2}

2 \times 2

4

\frac{1}{\sqrt{1 + 4}}

ⓘ Parentheses are computed first:

1 + 4

5

\frac{1}{\sqrt{5}}

By convention, we prefer numerical square roots in the numerator:

ⅰ

\frac{1}{\sqrt{5}}

\frac{\sqrt{5}}{5}

▶Result:

\frac{\sqrt{5}}{5}

The numeric value of:

\frac{\sqrt{5}}{5}

is:

\frac{\approx 2.2361}{5}

▷

\approx 0.4472