If θ=√2/2, what are the measures of θ if -360°≤θ≤360°?
4 answers
Correction: If sinθ=√2/2, what are the measures of θ if -360°≤θ≤360°?
sinθ > 0 in QI and QII.
so that means θ = -7π/4, -5π/4, π/4, 3π/4
so that means θ = -7π/4, -5π/4, π/4, 3π/4
from basics, you should know that √2/2 is the same as 1/√2
so you have sinθ = 1/√2
make it a point to have at your mathematical finger tips the sides of both the
45-45-90 degree and the 30-60-90 degree triangles,
from there that you will see that sin 45° = 1/√2
Secondly you know that the sine function is positive, like yours, in the first and second quadrants.
thus you solution is 45° and 180-45 or 135°
θ = 45° or θ = 135°
so you have sinθ = 1/√2
make it a point to have at your mathematical finger tips the sides of both the
45-45-90 degree and the 30-60-90 degree triangles,
from there that you will see that sin 45° = 1/√2
Secondly you know that the sine function is positive, like yours, in the first and second quadrants.
thus you solution is 45° and 180-45 or 135°
θ = 45° or θ = 135°
should have notice your domain is -360 <----> 360
so θ is also 45-360 and 135-360 which is
-315° and -225°
so θ is also 45-360 and 135-360 which is
-315° and -225°