Use your graphing calculator to find all radian solutions in the interval 0 ≤ x < 2𝜋 for each of the following equations. Round your answers to four decimal places.

Question

8 sin x - 5= 0

Answer 1

8sinx - 5 = 0

sinx = 5/8 = 0.625

x = sin^-1(.625) = 38.68218745 = 38.6822 degrees, rounded off to nearest 4 decimal places

for the 1st quadrant.

In the 2nd quadrant, x also = 180-38.6822 = 141.3178 degrees

but you want the answer in radians

x = 38.6822 times pi/180 = 0.2149 pi radians

or pi-.2149pi = 0.7851 pi radians

convert degrees to radians by multiplying by pi/180

sines are positive in quadrants 1 and 2