We read your photo as:

Copy and complete the table of values for y = 3 cos x, 30° <= x <= 330°. Using a scale of 2 cm to 30° on the x-axis and 2 cm to 1 unit on the y-axis, draw the graph of y = 3 cos x for 30° <= x <= 330°. Use the graph to: (i) solve 3 cos x = 0; (ii) find the minimum point.

Mathematics

ScanSolve AI Answer

Answers

2 parts
c(i)

x=90∘ and x=270∘x = 90^\circ \text{ and } x = 270^\circ

c(ii)

(180∘,−3.0)(180^\circ, -3.0)

Graph of y = 3cos(x)

Use the left and right arrow keys to trace the curve, up and down to jump between key points, and plus and minus to zoom.

Key points of y = 3cos(x)
Pointxy
x-intercept90°0
Minimum180°−3
x-intercept270°0

Step-by-step solution

3 steps

Here's the continuation of Question 6, focusing on parts (c)(i) and (c)(ii).

Part 6

The function is y=3cos⁡xy = 3 \cos x for 30∘≤x≤330∘30^\circ \le x \le 330^\circ.

Part c(i)

x=90∘ and x=270∘x = 90^\circ \text{ and } x = 270^\circ

solve 3cos⁡x=03 \cos x = 0;

Use your graph to

  1. Understand the equation 3cos⁡x=03 \cos x = 0.

    This equation is equivalent to y=0y = 0 on the graph of y=3cos⁡xy = 3 \cos x. We need to find the values of xx where the graph intersects the x-axis.

  2. Identify the x-intercepts from the table or graph.

    From the table of values (or by looking at the graph you would draw), y=0y = 0 when x=90∘x = 90^\circ and x=270∘x = 270^\circ.
    The solutions for 3cos⁡x=03 \cos x = 0 are x=90∘ and x=270∘\boxed{x = 90^\circ \text{ and } x = 270^\circ}.

Part c(ii)

(180∘,−3.0)(180^\circ, -3.0)

find the minimum point.

  1. Identify the minimum value of yy and its corresponding xx from the table or graph.

    The cosine function y=cos⁡xy = \cos x has a minimum value of −1-1. For y=3cos⁡xy = 3 \cos x, the minimum value will be 3×(−1)=−33 \times (-1) = -3.
    This minimum occurs when cos⁡x=−1\cos x = -1, which happens at x=180∘x = 180^\circ within the given range.
    From the table, at x=180∘x = 180^\circ, y=−3.0y = -3.0. This is the lowest point on the graph.
    The minimum point is (180∘,−3.0)\boxed{(180^\circ, -3.0)}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

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

Got a different question?Ask your own question