posted by ALISON on .
find all values of theta in the interval (0,360) that have the given value:
between 0 and 360°
(√2)/2 = 0.707 (approx.),
it would be much more visual to look at the form of the sine function between 0 and 360°.
Study the graph at the link (at the end of this post).
It is positive between 0 and 180° and negative for the rest of the interval, therefore between 180 and 360° there will not be a solution.
Between 0 and 180°, draw an imaginary horizontal line through y=0.7. This line will intersect the graph at two places, and precisely, at 60° and 120°.
The axis of symmetry is at 90°, so it is easy to remember (90-30)°=60°, and (90+30)°=120°.
You will use these angles very often in trigometry for the rest of your academic career, so it's worthwhile memorizing them.
Good explanation, but I think you want 45 deg.