Evaluate the following-i- sin-1 sin-4 ii- cos-1 cos2-3 iii- tan-1 tan-3

The correct option is D i. π4 , ii. 2π3 , iii. π3 We know that sin^ 1 ( sinθ )=θ , if π/2≤θ≤π/2 cos^ 1 (cosθ )=θ , if 0≤θ≤π ...

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Standard XII

Mathematics

Domain and Range of Basic Inverse Trigonometric Functions

Evaluate the ...

Question

Evaluate the following:
i. ${sin}^{- 1} (sin \frac{π}{4})$
ii. ${cos}^{- 1} (cos \frac{2 π}{3})$
iii. ${tan}^{- 1} (tan \frac{π}{3})$

- \frac{π}{4}

, ii.

- \frac{2 π}{3}

, iii.

- \frac{π}{3}

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\frac{3 π}{4}

,ii.

\frac{π}{3}

, iii.

\frac{2 π}{3}

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- \frac{3 π}{4}

, ii.

- \frac{π}{3}

, iii.

- \frac{3 π}{3}

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\frac{π}{4}

, ii.

\frac{2 π}{3}

, iii.

\frac{π}{3}

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Solution

The correct option is D i. $\frac{π}{4}$ , ii. $\frac{2 π}{3}$ , iii. $\frac{π}{3}$
We know that
${sin}^{- 1} (sin θ) = θ$ , if $- \frac{π}{2} \leq θ \leq \frac{π}{2}$
${cos}^{- 1} (cos θ) = θ$ , if $0 \leq θ \leq π$
and ${tan}^{- 1} (tan θ) = θ$ , if $- \frac{π}{2} < θ < \frac{π}{2}$
Hence,
i. ${sin}^{- 1} (sin π / 4) = \frac{π}{4}$
ii. ${cos}^{- 1} (cos 2 π / 3) = \frac{2 π}{3}$
iii. ${tan}^{- 1} (tan π / 3) = \frac{π}{3}$

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Similar questions

Q. Consider the following statement :
(i)

s i n^{- 1} (s i n \frac{2 π}{3}) = \frac{2 π}{3}

(ii)

t a n^{- 1} (t a n \frac{2 π}{3}) = \frac{- π}{3}

(iii)

c o s^{- 1} (c o s \frac{2 π}{3}) = \frac{2 π}{3}

(iv)

s e c^{- 1} (s e c \frac{5 π}{4}) = \frac{3 π}{4}

Q. Consider the following statement :
(i)

s i n^{- 1} (s i n \frac{2 π}{3}) = \frac{2 π}{3}

(ii)

t a n^{- 1} (t a n \frac{2 π}{3}) = \frac{- π}{3}

(iii)

c o s^{- 1} (c o s \frac{2 π}{3}) = \frac{2 π}{3}

(iv)

s e c^{- 1} (s e c \frac{5 π}{4}) = \frac{3 π}{4}

Q. Evaluate the following:
i.

{sin}^{- 1} (\frac{2 π}{4})

ii.

{cos}^{- 1} (cos \frac{7 π}{6})

iii.

{tan}^{- 1} (tan \frac{2 π}{3})

iv.

cos ({cos}^{- 1} (\frac{\sqrt{3}}{2}) + \frac{π}{6})

Q. If

z = \sqrt{3} + i

and

w = 3 i

Then

arg (z w)

and

arg \frac{w}{z}

Q. If

tan x = - \frac{3}{4},

\frac{3}{2} π < x < 2 π

then find the
i)

sin 2 x

ii)

cos 2 x

iii)

tan 2 x

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Evaluate the following:i. sin−1(sinπ4)ii. cos−1(cos2π3)iii. tan−1(tanπ3)

The correct option is D i. π4, ii.2π3 , iii. π3We know thatsin−1(sinθ)=θ, if −π2≤θ≤π2cos−1(cosθ)=θ, if 0≤θ≤πand tan−1(tanθ)=θ, if −π2<θ<π2Hence,i. sin−1(sinπ/4)=π4ii. cos−1(cos2π/3)=2π3iii. tan−1(tanπ/3)=π3

Evaluate the following:
i. ${sin}^{- 1} (sin \frac{π}{4})$
ii. ${cos}^{- 1} (cos \frac{2 π}{3})$
iii. ${tan}^{- 1} (tan \frac{π}{3})$