Question

How do you solve `sin(x + pi) = 0.5` between `0 < x < 2pi`?

Answer 1

Solve sin (x + pi) = 0.5

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

Explanation:

Trig table --> `sin (x + pi) = 0.5 = sin ((pi)/6)`
Trig unit circle gives another arc `(x + pi) = (pi - pi/6) = -pi/6`

a.`x + pi = pi/6 -> x = pi/6 - pi = (-5pi)/6`

b. `x + pi = pi - pi/6 = - pi/6`

On the trig circle, arc `(-5pi)/6` is the arc`(7pi)/6` and the arc `(-pi/6)` is the arc `((11p)/6)`