Find the principal value of cos−1x, for x=23.

If cos−1(23)=θ, then cosθ=23.Since we are considering principle branch, θ∈[0,π]. Also, since 23>0,θ being in first quadrant hence cos−1(23)=6π

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Find the principal value of ^{-1}x, for x={{3}}{2}.

Question

Find the principal value of $cos^{- 1} x,$ for $x = \frac{3}{2}$ .

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Theodore Discussed

Find the principal value of

cos^{- 1} x,

for

x = \frac{3}{2}

9 mins ago

Discuss this question LIVE

9 mins ago

cos^{- 1} (\frac{3}{2}) = θ

, then

cos θ = \frac{3}{2}

.
Since we are considering principle branch,

θ \in [0, π]

. Also, since

\frac{3}{2} > 0, θ

being in first quadrant hence

cos^{- 1} (\frac{3}{2}) = \frac{π}{6}

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Question Text	Find the principal value of $cos^{- 1} x,$ for $x = \frac{3}{2}$ .
Answer Type	Text solution:1
Upvotes	150