The diagram shows the graphs of y = tan x and y = cos x for 0 ≤ x ≤ π. The graphs intersect at points A and B. [Figure 5.1]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.

1. [M1] Use tan = sin/cos and multiply by cos tan x = cos x → sin x = cos²x
2. [M1] Use cos²x = 1 - sin²x sin x = 1 - sin²x
3. [M1] Attempt soln of quadratic in sinx. Ignore solution –1.618. Allow x = 0.618 sin x = 0.6180 . Allow (−1 + √5)/2
4. [A1] Must be radians. Accept 0.212π x-coord of A = sin¯¹0.618 = 0.666 cao
5. [M1] EITHER x-coord of B is π – their0.666 Expect 2.475(3). Must be radians throughout
6. [M1] y-coord of B is tan(their 2.475) or cos(their 2.475)
7. [A1] x = 2.48, y = -0.786 or -0.787 cao Accept x = 0.788π
8. [M1] OR y-coord of B is – (cos or tan (their 0.666))
9. [M1] x-coord of B is cos¯¹ (their y) or π + tan¯¹ (their y)
10. [A1] x = 2.48, y = -0.786 or -0.787 Accept x = 0.788π