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QUESTION

For each of the following, find all solutions in the interval [0, 2). Give all answers correct to .01 radians. If there is no solution, enter NONE.

3.  

For each of the following, approximate all angles θ in the interval [0°, 360°) that satisfy the equation. Give all angles to the nearest 0.1°. If there is no solution within a particular quadrant, enter NONE.

(a) sin θ = -0.2132 ° (quadrant I) ° (quadrant II)  ° (quadrant III) ° (quadrant IV)(b) cos θ = 0.8874 ° (quadrant I)  ° (quadrant II) ° (quadrant III)  ° (quadrant IV)(c) tan θ = 1.508 ° (quadrant I)  ° (quadrant II)  ° (quadrant III)  ° (quadrant IV)(d) cot θ = -0.9107 ° (quadrant I)  ° (quadrant II)  ° (quadrant III)  ° (quadrant IV)(e) sec θ = -1.192 ° (quadrant I)  ° (quadrant II) ° (quadrant III)  ° (quadrant IV)(f) csc θ = 2.74 ° (quadrant I) ° (quadrant II)  ° (quadrant III) ° (quadrant IV)

4.  

For each of the following, find all solutions. The variable n denotes a generic integer. (For each, select all that apply.)

1.  SEE IMAGE 4-A

(a)  

None of these

7π/4 + 2πn

5π/4 + 2πn

3π/4 + 2πn

π/4 + 2πn

2.  SEE IMAGE 4-B(b) 

π/3 + 2πn

π/6 + 2πn

π/6 + πn

None of these

π/3 + πn

(c)

3. sec(x) = 2

π/6 + 2πn

π/3 + 2πn

None of these

5π/3 + 2πn

π/6 + πn

(d) SEE IMAGE 4-D

5π/3 + 2πn

None of these

π/3 + 2πn

π/6 + πn

π/6 + 2πn

(e) SEE IMAGE 4-E

 3π/2 + 2πn 

ALL REAL NUMBERS - {π/2 + πn}

None of these

π/2 + πn

(f) 

SEE IMAGE 4-F

π/12 + πn

11π/12 + πn

π/6 + 2πn

None of these

11π/6 + 2πn

(g) SEE IMAGE 4-G

  π/6 + πn

π/6 + 2πn

None of these

π/2 + 3πn

(h) SEE IMAGE 4-H

π/6 + 2πn

-π/12 + 2πn

5π/6 + 2πn

7π/12 + 2πn

None of these

(i) SEE IMAGE 4-I

7π/12 + πn

π/4 + πn

5π/6 + 2πn

7π/6 + 2πn

None of these

(j) 2 cos(x) + 1 = 0

None of these

π/6 + 2πn

π/3 + 2πn

2π/3 + 2πn

4π/3 + 2πn

(k) (cos(x) - 1)(sin(x) + 1) = 0

None of these

2πn

π/4 + 2πn

3π/2 + 2πn

π/2 + 2πn

(l) sec2(x) - 4 = 0

π/3 + 2πn

5π/3 + 2πn

4π/3 + 2πn

2π/3 + 2πn

None of these

(m)     cot2(x) - 3 = 0

None of these

π/6 + πn

5π/6 + πn

π/3 + πn

π/3 + 2πn

(n)    

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