The principal value of cos -1-sin7 -6 is

The correct option is C π/3cos^ 1( sin7π/6 )=cos^ 1{cos(π/2+7π/6 )} cos^ 1(cos5π/3 )=cos^ 1{cos(2π 5π/3 )} =cos^ 1(cosπ/3 )=π/3 Remember, cos^ 1(cos x)=x, if 0 ...

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Byju's Answer

Standard XII

Mathematics

Modulus of a Complex Number

The principal...

Question

The principal value of $c o s^{- 1} (- s i n \frac{7 π}{6})$ is

5π/3

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7π/6

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π/3

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π/6

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Solution

The correct option is C
π/3

$c o s^{- 1} (- s i n \frac{7 π}{6}) = c o s^{- 1} {c o s (\frac{π}{2} + \frac{7 π}{6})}$
$c o s^{- 1} (c o s \frac{5 π}{3}) = c o s^{- 1} {c o s (2 π - \frac{5 π}{3})}$
$= c o s^{- 1} (c o s \frac{π}{3}) = \frac{π}{3}$
Remember, $c o s^{- 1} (c o s x) = x$ , if $0 \leq x \leq π$

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The correct option is C π/3cos−1(−sin7π6)=cos−1{cos(π2+7π6)} cos−1(cos5π3)=cos−1{cos(2π−5π3)} =cos−1(cosπ3)=π3 Remember, cos−1(cos x)=x, if 0≤x≤π

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