What is the value of arcsin(cos((7pi)/6)) ?

The value of arcsin(cos((7pi)/6)) is -pi/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

arcsin(cos((7pi)/6))

arcsin (cos (\frac{7 π}{6}))

- \frac{π}{3}

Decimal Notation

- 60

Solution steps

arcsin (cos (\frac{7 π}{6}))

Rewrite using trig identities:

cos (\frac{7 π}{6}) = sin (- \frac{2 π}{3})

cos (\frac{7 π}{6})

sin (\frac{π}{2} - x) = cos (x)

= sin (\frac{π}{2} - \frac{7 π}{6})

= sin (- \frac{2 π}{3})

= arcsin (sin (- \frac{2 π}{3}))

Use the inverse trig property:

- \frac{π}{3}

arcsin (sin (- \frac{2 π}{3}))

For

- \frac{π}{2} \leq x \leq \frac{π}{2}, a rcs in (s in (x)) = x

Rewrite using trig identities:

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

sin (- \frac{2 π}{3})

sin (x) = sin (π - (x))

= sin (\frac{2 π}{3} - π)

= sin (- \frac{π}{3})

= arcsin (sin (- \frac{π}{3}))

- \frac{π}{2} \leq - \frac{π}{3} \leq \frac{π}{2}

= - \frac{π}{3}

= - \frac{π}{3}

cos (60 0^{\circ})

sec (- 1)

arcsin (\frac{1}{2})

arcsin (\frac{1}{1.5})

sin (2 \cdot \frac{π}{2})

What is the value of arcsin(cos((7pi)/6)) ?
The value of arcsin(cos((7pi)/6)) is -pi/3