Solve the equation for all degree solutions and if 0° ≤ θ < 360°. Do not use a calculator (Enter your answers as a comma-separated list. If there is no solution, write no solution.)

1. 2 sin θ = root 2

(a) all degree solutions (let k be any integer.)

(b) 0≤ θ < 360°

2. 2 cos θ - root 3=0

(a) All degree solutions (let k be any integer.)

(b) 0≤ θ < 360°

3. root 3 cot θ - 1=0

(a) all degree solutions (Let k be any integer.)

(b) 0° ≤ θ < 360°

1.-

a) θ = 45 ° + 360k

θ = 135° + 360k

b) θ = 45 ° 0 ≤ θ < 360°

θ = 135°

2.-

a) θ = 30° + 360k

θ = 330° + 360k

b) θ = 30° 0 ≤ θ < 360°

θ = 330°

3.-

a) θ = 60° + 360k

θ = 240° + 360k

b) θ = 60° 0 ≤ θ < 360°

θ = 240°

Step-by-step explanation:

1) 2 sin θ = √2

sin θ = √2/2

1. a) θ = 45 ° + 360k

θ = 135° + 360k

1. b) θ = 45 ° 0 ≤ θ < 360°

θ = 135°

2.

2 cos θ - √3 = 0

2 cos θ = √3

cos θ = √3/2

2. a θ = 30° + 360k

θ = 330° + 360k

2. b θ = 30° 0 ≤ θ < 360°

θ = 330°

3. - √3 cot θ - 1 = 0

√3 cot θ = 1

cot θ = 1 / √3

3. a θ = 60° + 360k

θ = 240° + 360k

3. b θ = 60° 0 ≤ θ < 360°

θ = 240°