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$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 $0^o ≤ θ ≤ 360^o$

θ = 223 $^o$ , 305 $^o$

θ = 210 $^o$ , 330 $^o$

θ = 185 $^o$ , 345 $^o$

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 $^o$ )

∴ $θ = 218^o, 323^o$

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Use the graph of sin (θ) above to estimate the value of θ when sin (θ) = -0.6 for 0^o ≤ θ ≤ 360^o0^o ≤ θ ≤ 360^o