# Thread: Finding approximate solutions to equations

1. ## Finding approximate solutions to equations

Dear friends, please explain to me how to solve these problems.
Thank you!
1) Approximate to the nearest .1 degree all angles [theta] in the interval [0,360) that satisfy the equation sin(theta)=.7584
(might be more than one answer)

2) Approximate to the nearest .01 degree all angles [theta] on the onterval [0, 2pi) that satisfy the equation sin(theta)=.8412

Thank you!

2. In a unit circle, the y co-ordinate is $Sin{\theta}$.

If this is positive, then the y co-ordinate is above the x-axis.

If you draw a horizontal line through this y-axis value,
it cuts the circle in two places.

Calculating inverse sine gives you the acute angle the point on the circle makes with the positive x-axis.

As the situation is symmetrical, how do you calculate the answer that
your calculator does not give you?