Find the principal value of sin^-1\(\left( -\frac { 1 }{ 2 } \right) \)(in radians and degrees).

Find the principal value of sin^-1(2), if it exists.

Find the principal value of
 \({ Sin }^{ -1 }\left( \frac { 1 }{ \sqrt { 2 } } \right) \)

Find the period and amplitude of y = sin 7x

Sketch the graph of y = sin\((\frac{1}{3}x)\) for 0\(\le x <6\pi\).

For what value of x does sinx = sin⁻¹x?

Find the principal value of cos⁻¹\(\left( \frac { \sqrt { 3 } }{ 2 } \right) \)

Find cos^-1 \((-\frac{1}{\sqrt2})\)

Find all values of x such that -6\(\pi\le x \le 6\pi\) and cos x = 0 

State the reason for cos^-1\([cos(-\frac{\pi}{6})]\neq \frac{\pi}{6}.\)

Is cos^-1(-x) = \(\pi\)-cos⁻¹(x) true? Justify your answer.

Find the principal value of cos^-1\((\frac{1}{2})\).

Find the value of
\(2{ cos }^{ -1 }\left( \frac { 1 }{ 2 } \right) +{ sin }^{ -1 }\left( \frac { 1 }{ 2 } \right) \)

For what value of x, the inequality \(\frac { \pi }{ 2 } <{ cos }^{ -1 }(3x-1)<\pi \) holds?

Find the principal value of tan⁻¹(\(\sqrt3\))

Find the domain of the following functions :
\(tan^{-1}(\sqrt{9-x^{2}})\)

Find the value of
\(tan^{-1}(tan\frac{5\pi}{4})\)

Find the value of 
\(tan(tan^{-1}(\frac{7\pi}{4}))\)

Find the principal value of cosec⁻¹(−1)

Find the value of sec⁻¹\(\left( -\frac { 2\sqrt { 3 } }{ 3 } \right) \)

If cot^-1\(\frac{1}{7}=\theta\), find the value of cos \(\theta\).

Find the principal value of
sec^-1\((\frac{2}{\sqrt3})\)

Find the value of  \({ tan }^{ -1 }\left( \sqrt { 3 } \right) -{ sec }^{ -1 }(-2)\)

Prove that \(\frac{\pi}{2}\le sin^{-1}x+2 cos^{-1} x\le\frac{3\pi}{2}\)

Find the value of 
\(sin\left[ \frac { \pi }{ 3 } -{ sin }^{ -1 }\left( -\frac { 1 }{ 2 } \right) \right] \)

Prove that tan \(\left( { sin }^{ -1 }x \right) =\frac { x }{ \sqrt { 1-{ x }^{ 2 } } } for|x|<1\)

Prove that
 tan^-1\(\frac{1}{2}+tan^{-1}\frac{1}{3}=\frac{\pi}{4}\)

Solve tan^-1\(\left( \frac { 1-x }{ 1+x } \right) =\frac { 1 }{ 2 } { tan }^{ -1 }\) x for x > 0

Solve sin^-1 x > cos^-1x

Show that \(cot(sin^{ -1 }x)=\frac { \sqrt { 1-x^{ 2 } } }{ x } -1\le x\le 1\)and x \(\neq \) 0

Solve tan^-1 2x + tan^-1 3x = \(\frac{\pi}{4}\), if 6x² < 1

Solve \(tan^{ -1 }\left( \frac { x-1 }{ x-2 } \right) +tan^{ -1 }\left( \frac { x+1 }{ x+2 } \right) =\frac { \pi }{ 4 } \)

Find the value, if it exists. If not, give the reason for non-existence.
sin^-1(cos\(\pi\))

Find the period and amplitude of
y = -sin\((\frac{1}{3}x)\)

Find the period and amplitude of y = 4sin(−2x)

Find the value of \({ sin }^{ -1 }\left( sin\left( \frac { 5\pi }{ 4 } \right) \right) \)​

Find all values of x such that
-5\(\pi\le x \le 5\pi\) and cos x =1

Find the value of
\({ cos }^{ -1 }\left( \frac { 1 }{ 2 } \right) +{ sin }^{ -1 }(-1)\)

Find the value of \({ cos }^{ -1 }\left( cos\frac { \pi }{ 7 } cos\frac { \pi }{ 17 } -sin\frac { \pi }{ 7 } sin\frac { \pi }{ 17 } \right) .\)

Find the domain of
g(x) = sin⁻¹x + cos⁻¹x

Find the domain of the following functions
\(\frac{1}{2}tan^{-1}(1-x^2)-\frac{\pi}{4}\)

Find the value of \(\tan^{-1}(tan(-\frac{\pi}{6}))\)

Find the value of 
tan (tan⁻¹(1947))

Find the value of 
tan(tan^-1(-0.2021)).

Find the principal value of
cot^-1 \((\sqrt{3})\)

Find the principal value of
cosec^{-1\((-\sqrt{2})\)}

Find the value, if it exists. If not, give the reason for non-existence
\({ tan }^{ -1 }\left( sin\left( -\frac { 5\pi }{ 2 } \right) \right) \)

Find the value, if it exists. If not, give the reason for non-existence.
sin^-1 [sin5]

Find the principal value of \({sin }^{ -1 }\left( sin\left( -\frac { \pi }{ 3 } \right) \right) \)

Find the principal value of \({sin }^{ -1 }\left( sin\left( \frac { 5\pi }{ 6 } \right) \right) \)

Find the value of \(cos\left[ \frac { 1 }{ 2 } { cos }^{ -1 }\left( \frac { 1 }{ 8 } \right) \right] \) 

Prove that 2tan^-1\(\frac{1}{2}+tan^{-1}\frac{1}{7}=tan^{-1}\frac{31}{17}\)

Find the principal value of
sec⁻¹(−2).

Find the value of \({ sin }^{ -1 }\left( sin\left( \frac { 2\pi }{ 3 } \right) \right) \)

Find cos^-1\((cos(-\frac{\pi}{3}))\)

Find cos^-1\((cos(\frac{7\pi}{6}))\)

Find the principal value of cot^-1 \((\sqrt 3)\)