SOLUTION: Use the unit circle to find all values of θ between 0 and 2π for which the given statement is true. (Enter your answers as a comma-separated list.) sin θ = 1/2 &

Algebra ->  Trigonometry-basics -> SOLUTION: Use the unit circle to find all values of θ between 0 and 2π for which the given statement is true. (Enter your answers as a comma-separated list.) sin θ = 1/2 &      Log On


   

Question 1074713: Use the unit circle to find all values of θ between 0 and 2π for which the given statement is true. (Enter your answers as a comma-separated list.)
sin θ = 1/2
θ = rad
Found 3 solutions by Alan3354, KMST, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
did you look at the unit circle?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the unit circle with an inscribed regular hexagon divided into 6 equal "pizza slices" (at least for American pizza pies).

Each "slice" is an equilateral triangle, with 3 congruent angles,
each measuring pi%2F3 (since they add to half a turn =pi radians),
and 3 congruent sides, each with length 1 .
Two of those equilateral triangle are split into 2 congruent right triangles,
so the height of those triangles is 1%2F2 ,
and the angles marked with small arcs have sin%28theta%29=1%2F2 .
Those angles measure theta=%281%2F2%29%28pi%2F3%29=highlight%28pi%2F6%29 ,
but since angles are measured counterclockwise from the positive x-axis,
the angle marked with the red arc is pi-pi%2F6=highlight%28pi%2F6%29 .

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Use the unit circle to find all values of θ between 0 and 2π for which the given statement is true. (Enter your answers as a comma-separated list.)
sin θ = 1/2
θ = rad
Find a unit circle and look it up! 

One angle is in the 1st quadrant, and the other is in the 2nd quadrant.