1.45: Cosine graph and shaded area

0606/12/O/N/16 — Question 7 · 8 marks

1.45 diagram

The diagram shows part of the graph of

y = 2\cos\left(x - \dfrac{\pi}{6}\right)

. The graph intersects the

y

-axis at the point

A

, has a maximum point at

B

and intersects the

x

-axis at the point

C

.

(i)

Find the coordinates of

A

.

[1]

(ii)

Find the coordinates of

B

.

[2]

(iii)

Find the coordinates of

C

.

[2]

(iv)

Find

\displaystyle\int 2\cos\left(x - \dfrac{\pi}{6}\right)\,\mathrm{d}x

.

[1]

(v)

Hence find the area of the shaded region.

[2]