Recover a sinusoidal rule from graph features

Practise recover a sinusoidal rule from graph features with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

A function has form $f(x)=a\sin(bx)+d$, with $a,b>0$. Its maximum is 7, minimum is 1, and period is $\pi$. (a) Find a, b and d. [3 marks] (b) Find the first positive x where f reaches its maximum. [1 marks]

Worked explanation

• Part (a)

  The amplitude is $(7-1)/2=3$ and midline is $(7+1)/2=4$. Since period $2\pi/b=\pi$, $b=2$.

• Part (b)

  The first maximum occurs when $2x=\pi/2$, hence $x=\pi/4$.

(a) $a=3$, $b=2$, $d=4$.; (b) $x=\pi/4$.

Original VectorPaths practice; not an official VCAA question or marking rubric.