Question

If θ=√2/2, what are the measures of θ if -360°≤θ≤360°?

Answer 1

Correction: If sinθ=√2/2, what are the measures of θ if -360°≤θ≤360°?

Answer 2

sinθ > 0 in QI and QII.

so that means θ = -7π/4, -5π/4, π/4, 3π/4

Answer 3

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°

Answer 4

should have notice your domain is -360 <----> 360

so θ is also 45-360 and 135-360 which is

-315° and -225°

Answer 5

[AI-generated answer — Explain Bot]

To find the measures of θ for the given range (-360° ≤ θ ≤ 360°), we need to consider the quadrants of the unit circle where the value of θ falls within this range.

Firstly, we know that θ = √2/2 represents an angle in standard position whose terminal side passes through a point with coordinates (√2/2, √2/2), which lies in the first quadrant.

To find the other angles within the given range, we can utilize the symmetry and periodicity properties of the unit circle:

1. First Quadrant: The given angle θ = √2/2 is already in the first quadrant.

2. Second Quadrant: The symmetrical angle in the second quadrant is 180° - θ.

3. Third Quadrant: The symmetrical angle in the third quadrant is 180° + θ.

4. Fourth Quadrant: The symmetrical angle in the fourth quadrant is 360° - θ.

Therefore, the measures of θ within the range -360° ≤ θ ≤ 360° are as follows:

- First Quadrant: θ = √2/2 (approximately 45°)
- Second Quadrant: 180° - θ = 180° - √2/2 (approximately 135°)
- Third Quadrant: 180° + θ = 180° + √2/2 (approximately 225°)
- Fourth Quadrant: 360° - θ = 360° - √2/2 (approximately 315°)

So, the measures of θ for -360° ≤ θ ≤ 360° are approximately 45°, 135°, 225°, and 315°.