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for questions 3 and 4, what values for theta(0 less than or equal to. theta. less than or equal to 2pi)

3. 3sin(theta) = sin(theta) -1
A. pi/3, 5pi/3

B. 2pi/3, 4pi/3

C. pi/6, 3pi/6

D. 7pi/6, 11pi/6

4. tan^2(theta) = -3/2 sec(theta)
A. pi/2, 5pi/2

B. 3pi/4, 5pi/4

C. pi/3, 5pi/3

D. 2pi/3, 4pi/3

Respuesta :

nobillionaireNobley
3.) 3sinθ = sinθ - 1
3sinθ - sinθ = -1
2sinθ = -1
sinθ = -1/2
θ = sin^-1(-1/2) = π + π/6, 2π - π/6 = 7π/6, 11π/6

4.) tan^2 θ = -3/2 sec θ
sin^2 θ / cos^2 θ = -3/2(1/cos θ)
sin^2 θ / cos θ = -3/2
1 - cos^2 θ = -3/2 cos θ
cos^2 θ - 3/2 cos θ - 1 = 0
2cos^2 θ - 3cos θ - 2 = 0
2cos^2 θ - 4cos θ + cos θ - 2 = 0
2cos θ (cos θ - 2) + 1(cos θ - 2) = 0
(2cos θ + 1) = 0 or (cos θ - 2) = 0
cos θ = -1/2 or cos θ = 2            [but cos θ can never be 2]
θ = cos^-1(-1/2) = π - π/3, π + π/3 = 2π/3, 4π/3