What are the solutions to the equation sin (x+7π/2) = - √3/2 over the interval [0,2π]?

Answer 1

Hello, the video I have made is a little on the long side but I wanted to explain the why of this question and the how of finding solutions more generally.

Rather than memorizing any formulas, it helps to understand what sin and cos really are. This will help you understand how to find a solution rather than requiring you to memorize the unit circle.

Simple memorization often fails us when confronted with a stressful environment like a test or when needing to be used in a new context.

Answer 2

sin(x+7pi/2) = -sqr3/2

x + 7pi/2 = sin^-1(-sqr3/2) = 300 degrees or 5pi/3 radians or 210 degrees or 4pi/3

x = 5pi/3 - 7pi/2 = -11pi/6 in quadrant IV or 7pi/6 in quadrant III

x = 4pi/3 - 7pi/2 = 8pi/6 -21pi/6 = -13pi/6 or 11pi/6

x= pi/6 or 11pi/6 radians

or

x =30 or 330 degrees

check the answers:

7pi/2 = 3.5pi = 3pi/2= 270 degrees

30+270 =300, sin300 = -sqr3/2

330+270=600, 600-360 = 240, sin240=-sqr3/2