Consider the function

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

f(x)=a\tan(2x)+b

, where

x\neq\frac{(2n+1)\pi}{4}

n\in\mathbb{Z}

and

a,b\in\mathbb{R}

. The graph of

y=f(x)

passes through the points

\left(\frac{\pi}{12},5\right)

and

\left(\frac{\pi}{3},7\right)

. (a) Write down the period of

f

. (b) Find the value of

a

and the value of

b