What is the value of arccos(sin(-(7pi)/6)) ?

The value of arccos(sin(-(7pi)/6)) is pi/3

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arccos(sin(-(7pi)/6))

arccos (sin (- \frac{7 π}{6}))

\frac{π}{3}

Solution steps

arccos (sin (- \frac{7 π}{6}))

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{7 π}{6}) = - sin (\frac{7 π}{6})

= arccos (- sin (\frac{7 π}{6}))

Rewrite using trig identities:

sin (\frac{7 π}{6}) = - sin (\frac{5 π}{6})

= arccos (- (- sin (\frac{5 π}{6})))

Simplify

= arccos (sin (\frac{5 π}{6}))

Rewrite using trig identities:

sin (\frac{5 π}{6}) = sin (\frac{π}{6})

= arccos (sin (\frac{π}{6}))

Rewrite using trig identities:

sin (\frac{π}{6}) = cos (\frac{π}{3})

= arccos (cos (\frac{π}{3}))

Use the inverse trig property:

\frac{π}{3}

= \frac{π}{3}

arctan (\frac{2}{- 3})

sin (7 5^{\circ}) cos (1 5^{\circ}) + cos (7 5^{\circ}) sin (1 5^{\circ})

sin (arctan (- 5))

tan (\frac{2}{2})

arccos (- 2)

What is the value of arccos(sin(-(7pi)/6)) ?
The value of arccos(sin(-(7pi)/6)) is pi/3