# trig

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

sintheta= √2
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2

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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.

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2. Good explanation, but I think you want 45 deg.

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