Use the graph of sin (θ) below to estimate the value of θ when sin
MATHEMATICS
JAMB 2023
Use the graph of sin (θ) below 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: D.θ = 218\(^o\), 323\(^o\)
Explanation
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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