Shape and Space 10

4 marks · Normal

The function is plotted for angles from to .

(a)

On the axes below, sketch the graph of for .

Axes for \( y = \cos \theta \) graph. Sketch with labelled key points.

[2 marks]

(b)

Write down the value of between and for which is at its minimum.

[1 mark]

(c)

State the period of the function in degrees.

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) — · must show Correct shape, Labels at

(b) 180 degrees

Must show: Sketch with correct shape and labels, Minimum value at 180 degrees, Period = 360 degrees

Common mistakes: Incorrect position of minimum; Wrong sketching of shape

Show mark scheme and worked solution

Marking points

B1 (a) · 2 marks · Sketch correct and shows the curve passes through the points: (0,1), (90,0), (180,-1), (270,0), (360,1), with axes labelled.

B2 (b) · 1 mark · Correctly states as where is minimum.

B3 (c) · 1 mark · States the period is 360 degrees.

Worked solution

a) The cosine graph starts at (0,1), passes through (90,0), (180,-1), (270,0), and returns to (360,1).

b) The minimum is at , where .

c) The period is 360 degrees because the graph repeats every 360°.