Question

Sin x/7=-3square root/2

Answer 1

I will read that as sin (x/7) = -√3/2 since √3/2 is one of the trig values I recognize


So x/7 must be in quadrants III or IV

I know sin 60° = +√3/2
so my angle in "standard position " is 60°

x/7 = 180+60 = 240
x = 1680°
or
x/7 = 360-60 = 300
x = 4200°

but the period of sin (x/7) = 360/(1/7) = 2520°

<b>so general solution
x = 1680°+2520k°
x = 4200°+2520k°</b>

testing:
let k = 4
x = 11760
sin 11760/7 = -.866025... and -√3/2 =-.866025..