3.3: Sine curve constants and minimum

0606/12/F/M/22 — Question 3 · 8 marks

The curve with equation

y = a\,\mathrm{sin}\,bx + c

, where

a

b

and

c

are constants, passes through the points

\left(\dfrac{\pi}{4}, 11\right)

and

\left(\dfrac{3\pi}{4}, -5\right)

. It is given that

\mathrm{sin}\,bx

has period

\dfrac{\pi}{16}

(a)

Find the exact values of

a

b

and

c

[4]

(b)

Using your answer to part (a), find the coordinates of the minimum point on the curve for

0 \leqslant x \leqslant \dfrac{\pi}{16}

[4]