Exam 33: Solving Trigonometric Equations

Determine whether the statement is true or false.Justify your answer. ​ The equation $2 \sin 4 t - 1 = 0$ has four times the number of solutions in the interval [0,2π)as the equation $2 \sin t - 1 = 0$ . ​

Use inverse functions where needed to find all solutions (if they exist)of the given equation on the interval [0,2π).​ $2 \cos ^ { 2 } x - \cos x - 1 = 0$ ​

Solve the following equation. $\tan ^ { 4 } x - 1 = 0$

Solve the following equation.​ $8 \sin ^ { 2 } 2 x = 4$ ​

Solve the multiple-angle equation.​ $2 \sec 4 x = 4$ ​

Use inverse functions where needed to find all solutions of the equation in the interval [0,2π).​ $\cot ^ { 2 } x - 25 = 0$ ​

Solve the following equation.​ $\tan 3 x ( 8 \tan x - 8 ) = 0$ ​

Solve the following equation.​ $5 \sqrt { 3 } \csc x - 10 = 0$ ​

Solve the multiple-angle equation. $\tan \frac { x } { 2 } = \frac { \sqrt { 3 } } { 3 }$

Find all solutions of the following equation in the interval [0,2π).​ $4 \tan x + 4 \sqrt { 3 } = 0$ ​

Solve the following equation. ​​ $10 \sin x + 5 = 0$ ​

Solve the following equation.​ $\left( 3 \tan ^ { 2 } x - 3 \right) \left( \tan ^ { 2 } x - 3 \right) = 0$ ​

Use a graphing utility to approximate the solutions (to three decimal places)of the given equation in the interval $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ . ​​ $6 \sin 2 x - 8 \cos x + 9 \sin x = 6$ ​

Solve the following equation.​ $\sin x ( 5 \sin x + 5 ) = 0$ ​