WMA11 Jan 2023

• WMA11/01 (Edexcel) IAL P1 January 2023, Q9, Graphs of Trigonometric Functions, Tangent

​​ 

Figure 3 shows a sketch of

• the curve with equation​​ y=tan⁡x

• the straight line 1 with equation​​ y =πx

in the interval​​ -π < x < π

• State the period of​​ tan⁡x

(1)

• Write down the number of roots of the equation

  • tan⁡x​​ = (π​​ + 2)​​ x​​ in the interval -π < x < π

(1)

• • tan⁡x=πx​​ in the interval -2π < x < 2π

(1)

• tan⁡x=πx​​ in the interval -100​​ π​​ < x < 100​​ π

(1)

SOLUTION

a- ​​ The period of tan is​​ π.

b-i-​​ The line of y=(π​​ + 2)​​ x​​ would be more steeper than​​ y=πx​​ and the line must look something like as shown below.​​ 

Therefore, the answer is 3.​​ 

ii-​​ As the line would intersects once between 0 and π. Therefore, from ​​ π to 2π, there will be one more intersection between line ans curve. So, overall from 1 to 2π, there will be 2 points of intersections. Similarly, there will be another two intersection between the 0 and -2π. It is important to note that the line wouldn’t meet x axis anywhere after the origin point.​​ 

Therefore, the answer​​ 

2+1+2=5​​ 

iii-​​ as from the above part, it ​​ is known that from 0 to π, there are 1 points of intersection. Therefore, there will be 50 points of intersection between o to 50π. And, similarly there will be 50 points of intersection between 0 to - 50π. Hence, the total point of intersection between -100π to 100π is​​ 

100+1+100=201

Don’t forget to consider the point of intersection at the origin point which doesn’t repeat anywhere else in between -100π to 100π.​​