Solve the equation 8sin(1/2)x - 5 = 0 for 0 < x < 2pi. Round your answers to the nearest hundredth of a radian.

Question

Solve the equation 8sin(1/2)x - 5 = 0 for 0 < x < 2pi. Round your answers to the nearest hundredth of a radian.

Answer 1

8 sin(x/2) - 5 = 0   for 0 < x < 2pi

 

8 sin(x/2) = 5

sin(x/2) = 5/8

x/2 = sin^-1(5/8)

 

x = 2·sin^-1(5/8)

 

Use you calculator to get the answer.  Be sure it's set to radians, not degrees. There are actually two answers on the interval 0<x<2pi, one in the first quadrant (which your calculator gives you) and one in the second quadrant at pi-x radians.

Answer 2

8 sin(x/2) - 5 = 0

 

sin(x/2) = 5/8

 

In radians,

 

x/2 = arcsin(5/8)

 

x/2 ≅ 0.67513

or 

x/2 ≅ π - 0.67513 = 2.46646

 

x = 2(0.67513) = 1.35026

or

x = 2(2.46646) = 4.93292

 

Test the answers.