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Complete the table for values of y = 2 cos x and y = 3 sin x, correct to 1 decimal place.

Mathematics

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a) Complete the table for values of y=2cos⁡xy = 2 \cos x and y=3sin⁡xy = 3 \sin x, correct to 1 decimal place.

  1. Calculate values for y=2cos⁡xy = 2 \cos x.

    • For x=0∘x = 0^\circ, y=2cos⁡0∘=2(1)=2.0y = 2 \cos 0^\circ = 2(1) = 2.0.
    • For x=30∘x = 30^\circ, y=2cos⁡30∘=2(32)=3≈1.7y = 2 \cos 30^\circ = 2(\frac{\sqrt{3}}{2}) = \sqrt{3} \approx 1.7.
    • For x=60∘x = 60^\circ, y=2cos⁡60∘=2(12)=1.0y = 2 \cos 60^\circ = 2(\frac{1}{2}) = 1.0.
    • For x=90∘x = 90^\circ, y=2cos⁡90∘=2(0)=0.0y = 2 \cos 90^\circ = 2(0) = 0.0.
    • For x=120∘x = 120^\circ, y=2cos⁡120∘=2(−12)=−1.0y = 2 \cos 120^\circ = 2(-\frac{1}{2}) = -1.0.
    • For x=150∘x = 150^\circ, y=2cos⁡150∘=2(−32)=−3≈−1.7y = 2 \cos 150^\circ = 2(-\frac{\sqrt{3}}{2}) = -\sqrt{3} \approx -1.7.
    • For x=180∘x = 180^\circ, y=2cos⁡180∘=2(−1)=−2.0y = 2 \cos 180^\circ = 2(-1) = -2.0.
    • For x=210∘x = 210^\circ, y=2cos⁡210∘=2(−32)=−3≈−1.7y = 2 \cos 210^\circ = 2(-\frac{\sqrt{3}}{2}) = -\sqrt{3} \approx -1.7.
    • For x=240∘x = 240^\circ, y=2cos⁡240∘=2(−12)=−1.0y = 2 \cos 240^\circ = 2(-\frac{1}{2}) = -1.0.
    • For x=270∘x = 270^\circ, y=2cos⁡270∘=2(0)=0.0y = 2 \cos 270^\circ = 2(0) = 0.0.
    • For x=300∘x = 300^\circ, y=2cos⁡300∘=2(12)=1.0y = 2 \cos 300^\circ = 2(\frac{1}{2}) = 1.0.
    • For x=330∘x = 330^\circ, y=2cos⁡330∘=2(32)=3≈1.7y = 2 \cos 330^\circ = 2(\frac{\sqrt{3}}{2}) = \sqrt{3} \approx 1.7.
    • For x=360∘x = 360^\circ, y=2cos⁡360∘=2(1)=2.0y = 2 \cos 360^\circ = 2(1) = 2.0.
  2. Calculate values for y=3sin⁡xy = 3 \sin x.

    • For x=0∘x = 0^\circ, y=3sin⁡0∘=3(0)=0.0y = 3 \sin 0^\circ = 3(0) = 0.0.
    • For x=30∘x = 30^\circ, y=3sin⁡30∘=3(12)=1.5y = 3 \sin 30^\circ = 3(\frac{1}{2}) = 1.5.
    • For x=60∘x = 60^\circ, y=3sin⁡60∘=3(32)≈2.6y = 3 \sin 60^\circ = 3(\frac{\sqrt{3}}{2}) \approx 2.6.
    • For x=90∘x = 90^\circ, y=3sin⁡90∘=3(1)=3.0y = 3 \sin 90^\circ = 3(1) = 3.0.
    • For x=120∘x = 120^\circ, y=3sin⁡120∘=3(32)≈2.6y = 3 \sin 120^\circ = 3(\frac{\sqrt{3}}{2}) \approx 2.6.
    • For x=150∘x = 150^\circ, y=3sin⁡150∘=3(12)=1.5y = 3 \sin 150^\circ = 3(\frac{1}{2}) = 1.5.
    • For x=180∘x = 180^\circ, y=3sin⁡180∘=3(0)=0.0y = 3 \sin 180^\circ = 3(0) = 0.0.
    • For x=210∘x = 210^\circ, y=3sin⁡210∘=3(−12)=−1.5y = 3 \sin 210^\circ = 3(-\frac{1}{2}) = -1.5.
    • For x=240∘x = 240^\circ, y=3sin⁡240∘=3(−32)≈−2.6y = 3 \sin 240^\circ = 3(-\frac{\sqrt{3}}{2}) \approx -2.6.
    • For x=270∘x = 270^\circ, y=3sin⁡270∘=3(−1)=−3.0y = 3 \sin 270^\circ = 3(-1) = -3.0.
    • For x=300∘x = 300^\circ, y=3sin⁡300∘=3(−32)≈−2.6y = 3 \sin 300^\circ = 3(-\frac{\sqrt{3}}{2}) \approx -2.6.
    • For x=330∘x = 330^\circ, y=3sin⁡330∘=3(−12)=−1.5y = 3 \sin 330^\circ = 3(-\frac{1}{2}) = -1.5.
    • For x=360∘x = 360^\circ, y=3sin⁡360∘=3(0)=0.0y = 3 \sin 360^\circ = 3(0) = 0.0.

    The completed table is:

    x∘0∘30∘60∘90∘120∘150∘180∘210∘240∘270∘300∘330∘360∘y=2cos⁡x2.01.71.00.0−1.0−1.7−2.0−1.7−1.00.01.01.72.0y=3sin⁡x0.01.52.63.02.61.50.0−1.5−2.6−3.0−2.6−1.50.0\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline x^\circ & 0^\circ & 30^\circ & 60^\circ & 90^\circ & 120^\circ & 150^\circ & 180^\circ & 210^\circ & 240^\circ & 270^\circ & 300^\circ & 330^\circ & 360^\circ \\ \hline y = 2 \cos x & 2.0 & 1.7 & 1.0 & 0.0 & -1.0 & -1.7 & -2.0 & -1.7 & -1.0 & 0.0 & 1.0 & 1.7 & 2.0 \\ \hline y = 3 \sin x & 0.0 & 1.5 & 2.6 & 3.0 & 2.6 & 1.5 & 0.0 & -1.5 & -2.6 & -3.0 & -2.6 & -1.5 & 0.0 \\ \hline \end{array}
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