Exam 33: Solving Trigonometric Equations

A Ferris wheel is built such that the height h (in feet)above the ground of a seat on the wheel at time t (in seconds)can be modeled by $h ( t ) = 67 + 54 \sin \left( \frac { \pi } { 18 } t - \frac { \pi } { 2 } \right)$ .The wheel makes one revolution every 36 seconds and the ride begins when t = 0.During the first 36 seconds of the ride,when will a person,who starts at the bottom of the Ferris wheel,be 67 feet above the ground? ​

Which of the following is a solution to the given equation? $2 \cos x - 1 = 0$

Use inverse functions where needed to find all solutions of the equation in the interval [0,2π).​ $\sec ^ { 2 } x - 6 \sec x = 0$ ​

The monthly sales S (in hundreds of units)of baseball equipment for an Internet sporting goods site are approximated by $S = 55.7 - 37.5 \cos \frac { \pi t } { 6 }$ where t is the time (in months),with t = 1 corresponding to January.Determine the months when sales exceed 7700 units at any time during the month.

Find all solutions of the following equation in the interval [0,2π).​ $3 \sec x - 3 \tan x = 3$ ​

Solve the following equation.​ $9 \cot ^ { 2 } x - 3 = 0$ ​

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

Solve the multiple-angle equation.​ $\cos \frac { 3 x } { 6 } = \frac { \sqrt { 2 } } { 2 }$ ​

Solve the following equation. ​ Secx - 2 = 0 ​

Solve the following equation.​ $2 \sin x - 1 = 0$

Find all solutions of the following equation in the interval [0,2π).​ $5 \sec x \csc x = 10 \csc x$ ​

The table shows the average daily high temperatures in Houston H (in degrees Fahrenheit)for month t,with t = 1 corresponding to January. Month, t Houston, H 1 62.3 2 66.3 3 73.3 4 79.3 5 85.3 6 90.3 7 93.3 8 93.4 9 89.3 10 82.3 11 72.3 12 64.3 Select the correct scatter plot from the above data.

Which of the following is a solution to the given equation?​ $2 \cos x - 1 = 0$ ​

Solve the multiple-angle equation.​ $\sin \frac { 3 x } { 6 } = - \frac { \sqrt { 3 } } { 2 }$ ​

Use the Quadratic Formula to solve the given equation on the interval [ $0 , \frac { \pi } { 2 }$ );then use a graphing utility to approximate the angle x.Round answers to three decimal places.​ $75 \cos ^ { 2 } x - 34 \cos x + 3 = 0$ ​

Solve the multiple-angle equation.​ $4 \tan 3 x = 4$ ​

Use a graphing utility to graph the function. ​​ $f ( x ) = \left( \sin ^ { 2 } x - \cos x \right)$ ​

Solve the following equation.​ $\cos 2 x ( 4 \cos x + 2 ) = 0$ ​

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

Which of the following is a solution to the given equation? ​ Cscx + 2 = 0 ​