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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)