Exam 6: Inverse Circular Functions and Trigonometric Equations

Solve the equation (x in radians and in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. - $\cos ^ { 2 } x + 2 \cos x = - 1$

Use a calculator to give the value to the nearest degree. - $\theta = \tan ^ { - 1 } ( - 0.7002 )$

Solve the equation (x in radians and in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. - $3 \csc ^ { 2 } \theta = 4 \csc \theta$

Graph the inverse circular function. - $y=\sin ^{-1} x$

Find the exact value of the real number y. - $y = \sin ^ { - 1 } ( 1 )$

Provide an appropriate response. - $\text { True or false? The statement } \tan \left( \tan ^ { - 1 } \mathrm { x } \right) = \mathrm { x } \text { for all real numbers in the interval } \leq x \leq \pi \text {. }$

Solve the equation for x, where x is restricted to the given interval. - $y = 3 \tan ( 2 x - 1 )$ , for $x$ in $\left( \frac { 1 } { 2 } - \frac { \pi } { 4 } , \frac { 1 } { 2 } + \frac { \pi } { 4 } \right)$

Solve the equation for exact solutions over the interval [0, 2 $[ 0,2 \pi )$ - $2 \sin ^ { 2 } x = \sin x$

Solve the equation for exact solutions. - $- \sin ^ { - 1 } ( 4 x ) = \frac { \pi } { 4 }$

Solve the equation for exact solutions. - $\cot ^ { - 1 } x + \cot ^ { - 1 } ( 1 + x ) = \frac { \pi } { 4 }$

Solve the equation for exact solutions over the interval [0, 2 $[ 0,2 \pi )$ - $\cos x = \sin x$

Solve the equation for exact solutions. - $\sin ^ { - 1 } x + \cos ^ { - 1 } \left( - \frac { 1 } { 2 } \right) = \pi$

Solve the equation for exact solutions. - $\arcsin x + 2 \arctan x = \pi$

Use a calculator to give the value to the nearest degree. - $\theta = \sin ^ { - 1 } ( 0.2079 )$

Use a calculator to give the value to the nearest degree. - $\theta = \cos ^ { - 1 } ( - 0.9397 )$

Use a calculator to give the value to the nearest degree. - $\theta = \cos ^ { - 1 } ( - 0.3907 )$

Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree. - $\sin 2 \theta + \sin \theta = 0$

Find the exact value of the real number y. - $y = \arcsin \left( - \frac { \sqrt { 3 } } { 2 } \right)$

Use a calculator to give the real number value. Round the answer to 7 decimal places. -y = arcsec (2.8842912)

Use a calculator to give the value to the nearest degree. - $\theta = \tan ^ { - 1 } ( 2.2460 )$