Question

How to solve for `x` in `sin(2x-pi/3)=1/2`?

how to solve sin(2x-Pi/3)=1/2 ?

Answer 1

`x = pi/4`

Explanation:

This might look intimidating, but we'll take this one step at a
time

`sin(2x-pi/3) = 1/2`

`2x-pi/3 = sin^-1(1/2)`

evaluate `sin^-1(1/2)` (you can read this great explanation here)

`2x - pi/3 = pi/6`

`2x = pi/6 + pi/3`

we need a common denominator

`2x = pi/6 + pi/3 xx 2/2`

`2x = (pi+2pi)/6`

`2x = (3pi)/6`

simplify

`2x = pi/2`

`x = (pi/2)/2`

`x = pi/2 xx 1/2`

`x = pi/4`

To check our work, let's graph the equation

graph{y +1/2= sin(2x-pi/3)}

Yes, there is an `x`-intercept at `(pi/4,0)` so we were right!