We read your photo as:

Complete the table and draw the graphs for y = 2 extcos x and y = 3 extsin x for x from 0^ exto to 360^ exto in intervals of 30^ exto.

Mathematics

ScanSolve AI Answer

Step-by-step solution

2 steps

Step 1: Complete the table for values of y=2cos⁡xy = 2 \cos x and y=3sin⁡xy = 3 \sin x.
We need to calculate the missing values for y=2cos⁡xy = 2 \cos x at x=240∘x = 240^\circ and for y=3sin⁡xy = 3 \sin x at x=270∘x = 270^\circ, correct to 1 decimal place.

For y=2cos⁡xy = 2 \cos x:
At x=240∘x = 240^\circ:

y=2cos⁡(240∘)=2×(−12)=−1.0y = 2 \cos(240^\circ) = 2 \times \left(-\frac{1}{2}\right) = -1.0

For y=3sin⁡xy = 3 \sin x:
At x=270∘x = 270^\circ:

y=3sin⁡(270∘)=3×(−1)=−3.0y = 3 \sin(270^\circ) = 3 \times (-1) = -3.0

The completed table is:

x∘x^\circ0∘0^\circ30∘30^\circ60∘60^\circ90∘90^\circ120∘120^\circ150∘150^\circ180∘180^\circ210∘210^\circ240∘240^\circ270∘270^\circ300∘300^\circ330∘330^\circ360∘360^\circ
y=2cos⁡xy = 2 \cos x21.710−1.0-1.0−1.7-1.7−2.0-2.0−1.7-1.7−1.0\mathbf{-1.0}01.01.72
y=3sin⁡xy = 3 \sin x01.52.632.61.50−1.5-1.5−2.6-2.6−3.0\mathbf{-3.0}−2.6-2.6−1.5-1.50

Step 2: Draw the graph of y=2cos⁡xy = 2 \cos x and y=3sin⁡xy = 3 \sin x.

Part a

Set up the axes on the provided grid. The x-axis should represent angles from 0∘0^\circ to 360∘360^\circ. A suitable scale would be 2 cm2 \, \text{cm} for 30∘30^\circ.

Part b

The y-axis should represent values from approximately −3.0-3.0 to 3.0. A suitable scale would be 2 cm2 \, \text{cm} for 1 unit.

Part c

Plot the points from the completed table for y=2cos⁡xy = 2 \cos x and draw a smooth curve through them. Label this curve y=2cos⁡xy = 2 \cos x.

Part d· 2 steps

Plot the points from the completed table for y=3sin⁡xy = 3 \sin x and draw a smooth curve through them. Label this curve y=3sin⁡xy = 3 \sin x.

  1. Use the graph to find the values of xx when 2cos⁡x−3sin⁡x=02 \cos x - 3 \sin x = 0.

    The equation 2cos⁡x−3sin⁡x=02 \cos x - 3 \sin x = 0 can be rewritten as 2cos⁡x=3sin⁡x2 \cos x = 3 \sin x.
    This means we need to find the x-coordinates of the intersection points of the two graphs, y=2cos⁡xy = 2 \cos x and y=3sin⁡xy = 3 \sin x.
    From the graph, locate the points where the two curves intersect.
    The intersection points occur at approximately:
    x≈33.7∘x \approx \boxed{33.7^\circ} and x≈213.7∘x \approx \boxed{213.7^\circ}

  2. Use the graph to find the values of yy when 2cos⁡x=3sin⁡x2 \cos x = 3 \sin x.

    This asks for the y-coordinates of the intersection points found in Step 3.
    At x≈33.7∘x \approx 33.7^\circ, read the corresponding y-value from either graph.
    y=2cos⁡(33.7∘)≈1.66≈1.7y = 2 \cos(33.7^\circ) \approx 1.66 \approx 1.7
    y=3sin⁡(33.7∘)≈1.66≈1.7y = 3 \sin(33.7^\circ) \approx 1.66 \approx 1.7
    At x≈213.7∘x \approx 213.7^\circ, read the corresponding y-value from either graph.
    y=2cos⁡(213.7∘)≈−1.66≈−1.7y = 2 \cos(213.7^\circ) \approx -1.66 \approx -1.7
    y=3sin⁡(213.7∘)≈−1.66≈−1.7y = 3 \sin(213.7^\circ) \approx -1.66 \approx -1.7
    The values of yy are approximately 1.7\boxed{1.7} and −1.7\boxed{-1.7}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp