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Use the graph of sin (θ) above to estimate the value o...
Use the graph of sin (θ) above to estimate the value of θ when sin (θ) = -0.6 for \(0^o ≤ θ ≤ 360^o\)

Use the graph of sin (θ) above to estimate the value of θ when sin (θ) = -0.6 for 0^o ≤ θ ≤ 360^o

A.

θ = 223^o, 305^o

B.

θ = 210^o, 330^o

C.

θ = 185^o, 345^o

D.

θ = 218^o, 323^o

Correct answer is D

On the y-axis, each box is \frac{1 - 0}{5} = \frac{1}{5} = 0.2unit

On the x-axis, each box is \frac{90 - 0}{6} = \frac{90}{6} = 15^o

θ_1 = 180^o + (2.5\times15^o) = 180^o + 37.5^o = 217.5^o ≃ 218^o (2 and half boxes were counted to the right of 180^o)

θ_2 = 270^o + (3.5\times15^o) = 270^o + 52.5^o = 322.5^o ≃ 323^o (3 and half boxes were counted to the right of 270^o)

θ = 218^o, 323^o