Question

How do you find the general solutions for `sin(x + π) = 0.5`?

Answer 1

Solve: sin (x + pi) = 0.5

Ans: `((7pi)/6)` and `((11pi)/6)`

Explanation:

Trig Table of Special Arcs -->
sin (x + pi) = 0.5 --> `x + pi = pi/6` and `x + pi = ((5pi)/6)`
a. `x + pi = pi/6` --> `x = pi/6 - pi = - ((5pi)/6)` or `((7pi)/6)`

b. `x + pi = ((5pi)/6)` --> `x = ((5pi)/6) - pi = - pi/6` `or ((11pi)/6)`

General solutions:
x = `((7pi)/6)` + `2kpi`
x = `((11pi)/6)` + `2kpi`