What is the value of arccos(0)+arcsin((sqrt(2))/2)+arctan(-1)+arccot(-(sqrt(3))/3) ?

The value of arccos(0)+arcsin((sqrt(2))/2)+arctan(-1)+arccot(-(sqrt(3))/3) is (7pi)/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

arccos(0)+arcsin((sqrt(2))/2)+arctan(-1)+arccot(-(sqrt(3))/3)

arccos (0) + arcsin (\frac{2}{2}) + arctan (- 1) + arccot (- \frac{3}{3})

\frac{7 π}{6}

Solution steps

arccos (0) + arcsin (\frac{2}{2}) + arctan (- 1) + arccot (- \frac{3}{3})

Use the following trivial identity:

arccos (0) = \frac{π}{2}

Use the following trivial identity:

arcsin (\frac{2}{2}) = \frac{π}{4}

Rewrite using trig identities:

arctan (- 1) = - \frac{π}{4}

Use the following trivial identity:

arccot (- \frac{3}{3}) = \frac{2 π}{3}

= \frac{π}{2} + \frac{π}{4} - \frac{π}{4} + \frac{2 π}{3}

Simplify

\frac{π}{2} + \frac{π}{4} - \frac{π}{4} + \frac{2 π}{3} : \frac{7 π}{6}

= \frac{7 π}{6}

6 sin (\frac{3 π}{4})

3 cos (\frac{1}{2})

cos (\frac{π}{5}) cos (\frac{π}{3}) - sin (\frac{π}{5}) sin (\frac{π}{3})

cos (π - 1)

arctan (\frac{90}{60})

What is the value of arccos(0)+arcsin((sqrt(2))/2)+arctan(-1)+arccot(-(sqrt(3))/3) ?
The value of arccos(0)+arcsin((sqrt(2))/2)+arctan(-1)+arccot(-(sqrt(3))/3) is (7pi)/6