Question

find all values of theta in the interval (0,360) that have the given value:

sintheta= √2
______
2

Answer 1

To find
sin(θ)=(√2)/2
between 0 and 360°
where
(√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.

http://www.google.ca/imgres?q=graph+sine+function&hl=en&sa=X&biw=1071&bih=625&tbm=isch&prmd=ivns&tbnid=OMu42wKsarjpBM:&imgrefurl=http://www.wsd1.org/waec/math/pre-calculus%2520advanced/Trigonometry/Graphing/graphingintro.htm&docid=ZDN6zUNT4oa-KM&w=641&h=341&ei=GgtmTrTcBaLs0gHoy6HRDQ&zoom=1&iact=hc&vpx=722&vpy=233&dur=1&hovh=164&hovw=308&tx=255&ty=121&page=2&tbnh=103&tbnw=194&start=12&ndsp=12&ved=1t:429,r:7,s:12

Answer 2

Good explanation, but I think you want 45 deg.